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Notation Index

Chapter I

(n, ~,P)-Probability triple, 1 (lR[C] denotes real [complex] field)

[a, b), (a, b], [a, b]-the usual half-open and closed intervals

E(X)-expectation of X, 8

C BS=Cauchy-Buniakowski-Schwarz, 8

iff = if and only if, 9

lR T-space of real functions on a set T, 11

R-Borel a-algebra of lR, 13

{(na,~a,Pa,gaß)a<ß: Ct,ß in D}-projective system, 17

X - usually a Banach space, X* its dual, X' its algebraic dual, 34

(i, X, B)-abstract Wiener triple, 41

Chapter 11

EB(X)-conditional expectation of X relative to a a-algebra ß, 64

PB = PIß, restriction of P to ß, 63

p B _ conditional probability relative to ß, 64

~(Y) or ~y- a-algebra generated by the given function Y, 75

V(I\)-maximum (minimum) operator, 105

(n, ~,ß, P(·I·))-Renyi's conditonal measure space, 104

E(Xtn+1 IXt1 , ... ,Xtn )-conditional expectation, 111

LP(n,Fs,p) = LP(Fs ), 111

.€g+ A = log+ A = log A for A > 1, = 0 for A ::; 1, 114

611

612 Notation Index

~v;, -Radon-Nikodym derivative of the P-continuous part of 1I, 142

Chapter III

CP, LP, C=, L=-Lebesgue spaces, 177

p(.) - a lifting map, 177

M= - space of real bounded measurable functions, 177

Ab.B - symmetrie difference of sets A and B, 178

Ta - evaluation functional, 183

Chapter IV

ß(T) = ßT - u-algebra of events prior to the optional T, 242

O:T(Xd = XT/\t - stopped process at T, 258

(}T(Xd = XT+t - translated process by T, 258

NA - nucleus operator, 324

Chapter V

[T1,T21 = ((t,w): T1(w):S: t:s: T2 (w)} - stochastic interval, 361

(X, Y) - quadratic covaration (continuous case), 376

[X, Yj - quadratic covariation (general case), 385

M,Mloc,Mc,A+ - classes ofprocesses, 377

LP(A),CP((X)) - spaces ofprocesses, 391

X t = Y 0 Tt or Yi = X 0 Tt- 1 - strict time change, 406

ß(~+) - Borel u-algebra of ~+, 4132

Chapter VI

Xi - the continuous part of a martingale, 448

S(D',O) - O-measurable simple functions, 462

Co - the Banach space of numerical sequences converging to zero, 470

b.Xt = X t - X t- - the jump of the process at t, 474

ey = {Et , tEl}, E t = B(D, F t , Y)-envelope of the Banach spaces of

Y-valued Ft-measurable bounded functions, 475

Notation Index

s(n, Ey) - normed vector space of "vector fields", 476

L'j;(P) - Orlicz space of Z-valued functions, 477

Mi(P) - subspace of L'j;(P) determined by simple functions, 477

x 02 = x ® x, tensor product of x, 479

[X] - quadratic variation of vector valued X, 480

(A)ij - the (i,j)th - element of an m-by-n matrix, 492

Xt - derived process of X t , 494 n

613

a=(al, ... ,an),ak = TI a7 i ,k=(k1 , ... ,kn ),lkl=k1 +···+kn ,512 i=1

Co (IR. n, IR.) - the space of real continuous functions on IR.n vanishing at

=, 528

Chapter VII

{HP, 11 . IIp} - Hardy space oflocal martingales, 540

{BMO, II·IIB} - the space of bounded mean oscillation for martingales,

540

H(Z) - dass of complex holomorphic processes, 544

Tx(M) - tangent space at x of a manifold M, 546 C( M) - the set of Coo - vector fields, 547

r~j - Christoffel symbol, 550

T~(M) = Tx(M) + iTx(M) - complexified tangent spae, 553

GL(M) - orthogonal frame bundle, 556

O(H) - bundle of orthogonal frames, 557

[Ai, A j ] = A;Aj - AjA;, the Lie bracket, 560

Ft - augmented filtration, 571

P* - augmented predictable a-algebra, 571

C6, C60 - dasses of two parameter processes, 576

Ms,.Afs - orthogonal complementary dasses of two parameter

martingales, 577

yaX - stochastic differential form, 578

X (81,82) - modified Brownian sheet, 580

Author Index

Author Index

Adams, C.R, 569 Alloin, C., 299 Ambrose, W., 168 Andersen, E.S., 142, 146, 148, 163 Anderson, RF., 527 Auslander, L., 585 Austin, D.G., 294, 331, 385

Bartle, RG., 485 Bell, D.R., 586 Belopol'skaya, Ya.1., 562, 586 Bharucha-Reid, A.T., 60 Bichteler, K., 475 Bismut, J.-M., 585 Blackwell, D., 259 Blake, L.H., 161 Blumenthai, RM., 509 Bochner, S., 10, 19, 20, 59, 112,

197, 330, 445, 456, 536 Bonami, A., 527 Borchers, D.R, 496, 522, 536 Bourbaki, N., 21, 31, 281 Brennan, M.D., 536, 569, 571,

574, 584, 586 Brooks, J.O., 443 Burkholder, D.L., 310

Cabaiia, E.M., 535 Cairoli, R, 564, 569, 570, 578, 586 Carmona, RA., 528 Cartan, H., 513 Cartier, P., 482 Chacon, RV., 442 Chang, D.K., 585 Choksi, J.R, 20, 23, 60, 220,

223, 231 Choquet, G., 328 Chow, Y.S., 70, 146, 157, 162,

211, 229, 231, 269, 281, 285, 330, 331

615

Chung, K.L., 194, 257, 330, 380, 424

Clarkson, J.A., 569 Coddington, E.A., 488 Cornea, A., 345, 440 Courrege, P., 389, 459, 479 Cramer, H., 389, 459, 479 Cuculescu, 1., 423, 430, 431, 443

Dalecky, Ju.L., 535, 562, 586 Dambis, K.E., 403, 411, 442 Darling, RW.R., 529 Davis, B.J., 300, 310 Davis, M., 26 de la Vallee Poussin, C.J., 79 Dellacherie, C." 363, 366, 373, 375,

475,509 Dinculeanu, N., 21, 92, 96, 102, 151,

155, 162, 311, 443, 470, 478 Doleans-Dade, C., 318, 363, 364,

366,439,441,442,530,535,571 Doob, J.L., 55, 75, 104, 115, 116,

122, 126, 134, 157, 163, 168, 171,191,194,197,230,257, 263, 291, 322, 330, 380, 424, 436, 442, 521

Dozzi, M., 574, 586 Dubins, L.E., 163, 413, 442 Dugundji, J., 229 Dunford, N., 92, 95, 96, 98, 99, 101,

106, 147, 151, 159, 178, 213, 214, 226, 279, 344, 389, 464, 470,534

Dym, H., 512, 536 Dynkin, E.B., 75, 151, 509

Eberlein, W.F., 213 Edgar, G.A., 252, 442 Emery, M., 553, 585

616

Fefferman, C.L., 301, 331 Feldman, J., 58 FeIler, W., 505 Fillmore, P.A., 228 Finetti, B.de, 1 Finlayson, H.C., 46 Fisk, D.L., 364, 418, 434, 442, 443 Flanders, H., 585 Föllmer, H., 369, 442, 543, 585 Freedman, D., 259 Freidlin, M., 587 Fremlin, D.H., 180

GangoIli, R., 482 Garsia, A.M., 300, 310, 312, 331 Gel'fand, I.M., 35, 36, 39 Getoor, R.K., 509, 541, 542, 585 Gikhman, I.L., 231 Girsanov, LV., 439 Girshick, M.A., 162 Gnedenko, B.V., 102 Goldberg, S., 585 Goldstein, J.A., 489 524 525 , , ,

536, 537 Gould, G.G., 389 Green, M.L., 586 Gross, L., 33, 41, 46, 58, 60 Guggenheim, H.W., 585 Gundy, R.F., 288, 310, 331

Hajek, J., 58, 116, 119 Halmos, P.R., 2, 11, 24, 55, 226 Hankel, H., 195 Hanner, 0., 176 Hardy, G.H., 69 Hayes, C.A., 229, 231 Helms, L.L., 263, 324, 330 Herz, C.S., 331 Hida, T., 47 Hille, E., 486 Hörmander, L., 559, 585 Hunt, G.A., 242, 322, 330

Author Index

Hürzeler, H.E., 586

Ikeda, N., 502, 529, 537, 559, 562, 583, 586

Ionescu Tulcea, A., 176, 185, 218,230

Ionescu Tulcea, C.T., 176, 185, 218, 224, 225, 226, 230, 231

Isaac, R., 134 Isaacson, D., 439 rtö, K., 36, 126, 334, 345, 419, 437,

442, 443, 521, 531

Jensen, B., 142, 146, 148, 154, 163 Johansen, S., 163 John, F., 312, 331 Johnson, G., 263, 324, 330

Kailath, T., 439 Kakutani, S., 537 Kampe de Feriet, J., 162 Kaneko, H., 583 Karhunen, K., 389 Karoui, N., 527 Karush, J., 163 Kazamaki, N., 432, 535 Kingman, J.F.C., 55 Knight, F.B., 411 Kolmogorov, A.N., 1, 10, 15, 16,35,

59, 102, 104, 112, 116, 121, 154, 162, 197, 200, 224, 389, 459,479

Krasnosel'skii, M.A., 156 Krinik, A., 527, 535 Kunita, H., 375, 384, 405, 442, 443,

529,535,537,582,587 Kuo, H.H., 535

Lamb, C.W., 289, 329, 331 Levinson, N., 488 Levy, P., 52, 55, 158, 163, 403 404 , ,

Author Index

482, 486 Licea, G., 440 Littlewood, J.E., 69, 291 Lohe, M., 146, 202 Loornis, L.H., 88, 423 Luzin, N., 326

MacKenzie, RE., 585 Maisonneuve, B., 439, 530 Malliavin, P., 560, 561, 585 Mallory, D.J., 55, 220 Marcinkiewicz, J., 122, 123 Maruyarna, G., 519 McKean, Jr., H.P., 436, 443 McShane, E.J., 97, 231, 443,

453, 454, 455, 456, 536 Mertens, J.-F., 230, 440 Metivier, M., 443, 503, 536 Meyer, P.-A., 126, 128, 227, 230,

259, 267, 328, 330, 348, 356, 363, 373, 390, 430, 432, 442, 443, 509, 535, 585

Millar, P.W., 330, 441 Millington, H., 19, 57 Minios, RA., 35, 39, 46 Molchan, G.M., 486 Morse, M., 585 Moy, S.-C., 155, 162

Nelson, E., 171, 231 Neumann, J. von, 228 Neveu, J., 202, 224, 231, 291, 431 Nirenberg, L., 312, 331 Nornoto, H., 47 Norris, J., 562 Nualart, D., 439, 528, 532

Olson, M.P., 163 Orey, S., 432, 439, 502

Paley, RE.A.C., 291, 459

Pardoux, E., 439,532 Panc, C.Y., 229, 231 Pellaurnail, J., 443, 503, 506 Petersen, K.E., 331 Phillips, RS., 496 Pitcher, T.S., 162 Poincare, H., 5 P61ya, G., 69 Postnikov, M.M., 585 Priouret, P., 257, 323

617

Prokhorov, Yu. V., 31, 32, 42, 281 Protter, P.E., 536

Rad6, T., 133, 431 Rao, K.M., 230, 369, 370, 433, 442 Reinhard, H., 527 Ren, Z.D., 156, 469, 470, 566 Renyi, A., 1, 104, 105, 116, 119 Riesz, F., 126, 498 Royden, H.L., 2, 21, 81, 197 Roynette, B., 527 Rutickii, Ya.B., 156 Ryan, R, 179,231

Saks, S., 326 Savage, L.J., 1, 162 Sazonov, V.V., 60, 102, 103, 218,

219,231 Schatten, R, 478, 480 Schreiber, B.M., 60 Schwartz, J.T., 92, 95, 96, 98, 99,

101, 106, 147, 151, 159, 178, 213, 214, 226, 279, 344, 389, 464, 470, 534

Schwartz, L., 35,66,231, 281, 583, 585

Schwarz, G., 403" 442 Segal, LE., 36, 60, 231 Shale, D., 50 Sharpe, M.J., 541, 542, 585 Sierpinski, W., 326, 328 Sion, M., 2, 19, 55, 57, 176,

618

178, 220, 230 Skorokhod, A.V., 231, 531 Snell, J.L., 269, 330 Stein, E.M., 291, 301, 331 Steinhaus, H., 154 Strassen, V., 162 Stratonovich, R.L., 418, 443 Stricker, C., 369, 432 Stroock, D.W., 527, 530, 535, 585 Subrahmanian, R., 161 Suchest on, L., 252, 442 Sudderth, W., 321 Sun, T.-C., 60 Sz.-Nagy, B., 498

Taniguchi, S., 562, 583 Transue, W., 585 Traynor, T., 176,178 Thlcea, (see Ionescu Thlcea)

Varadhan, S.R.S., 529, 530, 535 Vilenkin, N.Ya., 35, 39 Ville, J., 163

Walsh, J.B., 569, 570, 575,578, 580, 584, 586, 587

Watanabe, S., 126, 334, 345, 375, 384, 405, 419, 442, 502, 529, 536, 559, 562, 583, 586

Whitney, H., 547, 549 Wiener, N., 45, 46, 389, 443, 459 Wong, E., 576, 586 Wright, J.D.M., 97

Yaglom, A.M., 486 Yamasaki, Y., 50 Yeh, J., 46, 579, 586 Ylinen, K., 585 Yor, M., 422,443,527 Yosida, K.,. 537 Yushkevich, A.A., 509

Author Index

Zaanen, A.C., 231 Zakai, M., 439, 576, 586 Zygmund, A., 69, 123, 291, 459

619

SUBJECT INDEX A

A-analytie, 325 absolutely eontinuous (At)

relative to (Bt ), 382 abstract random variable, 1, 41 abstract Wiener spaee, 35, 526 aeeessible time, 361 aeeessible a-algebra, 362 adapted to a a-algebra, 110 adjunction proeedure, 98 adjoint operator, 81 admissible translate, 161 affine eonneetion, 555 a-stoehastie integral, 422 almost separable projeetive

system, 219 amart (=asymptotie martingale),

441 analytie manifold, 545 analytie (=A or Soustin)

operation, 325 A-(quasi, sub-) martingale, 570 approximate martingale, 159 A-proeess, 570 are length function, 548 assoeiated projeetive system, 279 asymptotie martingale, 441 atlas, 546 averaging identity, 84 averaging property, 69

B baekward integral, 422 Banaeh contraction mapping, 534 base of a martingale, 20 BMO, 233, 300 Borel-Cantelli lemma, 298 boundedly a-eomplete lattiee, 97 b-quadratie variation, 549

Brownian flow, 528 funetional, 576 motion (and density), 52 martingale eharacterization, 406 in a manifold, 551

Brownian sheet, 575 bundle of orthogonal frames, 557

unitary frames, 558

C ca,dlag, 230 canonical (= function space)

representation, 16 Caratheodory generated measure, 54 Cauchy distribution family, 52 Cauehy-Riemann equations, 544 CBS-inequality, 8 Cebysev inequality, 119 Chapman-Kolmogorov equation 505 characteristic function, 6

properties of, 51 characterization of projective limit

measures, 29 Brownian motion, 406

chart, 546 Christoffel symbols, 550 dass (D), (DL), 262 CP-manifold, 545 compatibility condition, 3

generalized, 17 compensator, 387 eomplex Brownian motion, 539 complex derivative of a process, 544 complex martingale, 540 conditional convergence theorem, 67

distribution, 153 formulas for, 153 expectation, 62, 64 characterization of, 85 generalized, 151 independence, 152, 574 Jensen inequality, 70

620

probability, 62, 64 as vector measure, 92 characterization of, 105 regularity of, 92

conditionally negative definite, 483

conformal basis, 543 martingale, 540 semimartingale, 540 on a manifold, 584

conjugate martingale, 540 connection, 550 coordinate neighborhood, 546 cotangent space, 547 control measure, 95 covariance function, 8 covariant differentiation, 555 cross section,176

local, 176 cylindrical prob ability, 36

D debut, 258 degenerate elliptic operator as

generator, 523 d-sequence, 290 tl-splitting, 289 density function, 7 diffeomorphic, 547 diffusion coefficient, 519

process, 519 direct sum property, 179 directed set, 16 discontinuity, point, 195

second kind, 194 distribution function, 2

joint, 3 Gaussian, 5 Poisson,6

distribution al solution, 580 Doob decomposition (discrete

case) , 126 Doob-Meyer decomposition

Subject Index

(continuous case), 233, 338 drift coefficient, 519 Dunford-Schwartz integral, 95

E c-(stochastic) partition, 397 event, 1 evolution equation, 506 expectation, 8

F Feller semigroup, 507

process, 507 F -quasimartingale, 583 fine covering, 211

essential covering, 211 finite subset property, 179 fixed point of discontinuity, 173 fundamental theorem of (stochastic) calculus, 437

G generalized Jordan

decomposition, 370 random process, 36

generator of a potential, 344 geodesic, 555 graph (of an optional), 362 grid, 569

H hermitian metric, 553 Hessian, 549 holomorphic complex process, 543

manifold, 546 real process, 578

horizontal lift , 557 space, 557

H-process, 570 H-quasimartingale, 570 hypoelliptic operator, 560

Subjeet Index

I image probability, 2 i-martingale, 571 inaeeessible time, 361 independent inerements, 9

mutually,9 o--algebras, 77

indicator funetion, 8 indistinguishable, 392 integration by parts for MeShave

integrals, 455 for symmetrie integral, 418

Itö's formula, (generalized), 395 for semimartingales, 448

Itö's integral, 391, 435

K Kähler manifold, 555 Kählerian metrie, 554 K.6t-eondition, 453 K -independenee, 154 Kolmogorov's inequality, 118 Kroneeker's lemma, 157

L Langevin type equation, 487 Laplaee-Beltrami operator, 551 Levy-Brownian motion, 482 L2 ,2-boundedness, 457 Lie derivative, 550 lifting, linear, 177 lifting map, 177

set, 179 topology, 228

Dill ,'P2-boundedness, 461 veetor ease, 476

LP'P-boundedness, 461 loeal eoordinate, 546 loeal martingale, 334 loealizability, 179

strietly, 179

M Malliavin eovarianee, 561 Markov ehain, 504

proeess, 503 strong,508 time reversed, 504

martingale, 20, 110

621

differenee (= inerement), 295 loeal, 334 regular, 269 semiregular, 269 wide sense, 111

martingale eonvergenee, 140, 148 MeShane's integral, 454 mean funetion, 8 mean square derivative, 489 measurable proeess, 171 measurable seminorm, 40 metrie tensor, 548 modelled after ]Rd, 546 modifieation of a proeess, 166 moving point of diseontinuity, 175 M-proeess, 567 multiplieation table (for

stoehastie differentials), 420

N natural (= predictable) proeess, 344 nearly a K.8t-eondition, 453 nonantieipative integrand, 471 normalization of H-proeess, 572 nucleus, 324

o one sided Fubini's theorem, 108 operation (A), 324 optimal stopping rule, 299

622

optional (= stopping time), 234 optional a-algebra, 362

sampling process, 239 (= well-measurable) process, 395

order eontinuous a-algebras, 208 Ornstein-Uhlenbeek sheet, 583 orthogonal frames, 556

bundle, 556 orthogonal inerements, 10 orthonormal basis of martingales,

543

p

parallel displaeement, 555 perfeet probability, 102 <1>-bounded, 584 point diseontinuity, 195 Polish spaee, 201 potential, 130 predietable (multivariate), 568

proeess, 337 a-algebra, 362 time, 361

pervisible (= predictable) time, 361

prineiple bundle, 557 P-rieh a-algebra, 70 proeess, canonieal

representation, 16 function spaee, 16

progressively measurable, 196 set, 258

projeetive limit of mappings, 29 projeetive limit of (signed,

veetor) measures, 19 system, 17 representation, 24 topologieal, 17

purely finitely additive, 147

Q quadratie variation, 318

Subject Index

generalized, 440 of L 2,2-bounded proeesses,

472 quasi-Ieft-eontinuous, 361 quasimartingale, 364

inequalities for, 434

R random linear mapping, 36

(field) funetion, 2 proeess, 1 Sehwartz distribution, 36 variable, 1

raw inereasing process, 387 realization (of a process), 2 reduee (strongly) a proeess, 436 regular, Baire, 21

Borel21 part of a set, 289

rieh a-algebra, 70 Riemannian metrie, 547 Riesz deeomposition, 126, 130 right (left) eontinuous filtration, 252

S sampie function, 2 semieompaet, 325 semimartingale (loeal), 364

ingegrals, 448 semiring, 11 semipotential, 371 semivariation, 94 separability of proeesses, 166 sequential maximality (s.m.), 19 set martingale, 20 S-independenee, 154 simple harmonie oseillator, 487 Skorokhod's integral, 531 Sobolev type norm, 467 Souslin operation, 324 speetral measure, 423 s-regular potential,355

Subject Index

stable distribution, 52 standard filtration, 334 stochastic base (= filtration

of adapted-process), 20 fiow, 528

stochastic differential equation (first order), 457

forms,578 * -representation, 423 stochastic integral, 389

integrator, 462 vector,477 interval, 361, 392 measure, 457 partition, 397 processes, 1 types, 7 strictly stationary, 7 weakly stationary, 8

stoppinig time ( = optional), 234 process, 234

Stratonovich's integral, 418 strong martingale, 571

law of large numbers, 121 type (p,p), 125

strongly normal, 539 sub (super) martingale, 111

semiregular, 269 subprocess, 567 sub (super) projective system, 280 super process, 567 symmetrie integral, 418

T tangent bundle, 547

space, 546 vectors, 546

thick set, 53 threads, 17 time change transformation, 405 times of discontinuity, 361 torsionfree connection, 550 totally inaccessible time, 361

tr= trace, 478 trajectory, 2

623

transition prob ability function, 506 stationary, 506

U uniform integrability, 115

terminal, 115, 213 unitary frame bundle, 557 universal separating set, 168 universally measurable set, 218 upcrossings inequality, 158

V variance function, 8 variation of a measure, 94 vector field, 547 Vitali condition "Vo", 211 V-process, 570 V-(quasi, sub) martingale, 570 V-strong submartingale, 571

W weak distribution, 36

martingale, 432, 570 weak solution, 580

type (1,1), 125 unit,85

weakly harmonizable process, 459 well measurable (= optional) pro­cess, 391 white noise, 487 Wiener-Brownian motion, 563 Wiener chaos, 531 Wiener distribution, 52

y

Young function, generalized, 460

Other Mathematics and Its Applications titles of interest:

P.M. Alberti and A. Uhlmann: Stochasticity and Partial Order. Doubly Stochastic Maps and Unitary Mixing. 1982, 128 pp. ISBN 90-277-1350-2

A.V. Skorohod: Random Linear Operators. 1983,216 pp. ISBN 90-277-1669-2

I.M. Stancu-Minasian: Stochastic Programming with Multiple Objective Functions. 1985,352 pp. ISBN 90-277-1714-1

L. Amold and P. Kotelenez (eds.): Stochastic Space-Time Models and Limit Theorems. 1985,280 pp. ISBN 90-277-2038-X

Y. Ben-Haim: The Assay of Spatially Random Material. 1985,336 pp. ISBN 90-277-2066-5

A. Pazman: Foundations ofOptimum Experimental Design. 1986,248 pp. ISBN 90-277-1865-2

P. Kree and C. Soize: Mathematics of Random Phenomena. Random Vibrations of Mechanical Structures. 1986,456 pp. ISBN 90-277-2355-9

Y. Sakamoto, M. Ishiguro and G. Kitagawa: Akaike Information Criterion Statis­tics. 1986,312 pp. ISBN 90-277-2253-6

GJ. Szekely: Paradoxes in Probability Theory and Mathematical Statistics. 1987, 264 pp. ISBN 90-277-1899-7

0.1. Aven, E.G. Coffman (Jr.) and Y.A. Kogan: Stochastic Analysis of Computer Storage. 1987,264 pp. ISBN 90-277-2515-2

N.N. Vakhania, V.I. Tarieladze and S.A. Chobanyan: Probability Distributions on Banach Spaces. 1987,512 pp. ISBN 90-277-2496-2

A.V. Skorohod: Stochastic Equationsfor Complex Systems. 1987,196 pp. ISBN 90-277-2408-3

S. Albeverio, Ph. Blanchard, M. Hazewinkel and L. Streit (eds.): Stochastic Processes in Physics and Engineering. 1988,430 pp. ISBN 90-277-2659-0

A. Liemant, K. Matthes and A. Wakolbinger: Equilibrium Distributions of Branching Processes. 1988,240 pp. ISBN 90-277-2774-0

G. Adomian: Nonlinear Stochastic Systems Theory and Applications to Physics. 1988,244 pp. ISBN 90-277-2525-X

J. Stoyanov, O. Mirazchiiski, Z. Ignatov and M. Tanushev: Exercise Manual in Probability Theory. 1988,368 pp. ISBN 90-277-2687-6

E.A. Nadaraya: Nonparametric Estimation of Probability Densities and Regression Curves. 1988,224 pp. ISBN 90-277-2757-0

H. Akaike and T. Nakagawa: Statistical Analysis and Control of Dynamic Systems. 1998,224 pp. ISBN 90-277-2786-4

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V. Paulauskas and A. Rackauskas: Approximation Theory in the Central Limit Theorem. Exact Results in Banach Spaces. 1989, 176 pp. ISBN 90-277-2825-9

R.Sh. Liptser and A.N. Shiryayev: Theory of Martingales. 1989,808 pp. ISBN 0-7923-0395-4

S.M. Ermakov, V.V. Nekrutkin and A.S. Sipin: Random Processes for Classical Equations of Mathematical Physics. 1989, 304 pp. ISBN 0-7923-0036-X

G. Constantin and I. Istratescu: Elements of Probabilistic Analysis and Applica­tions. 1989,488 pp. ISBN 90-277-2838-0

S. Albeverio, Ph. Blanchard and D. Testard (eds.): Stochastics, Algebra and Analysis in Classical and Quantum Dynamies. 1990, 264 pp. ISBN 0-7923-0637-6

Ya.I. Belopolskaya and Yu.L. Dalecky: Stochastic Equations and Differential Geometry. 1990,288 pp. ISBN 90-277-2807-0

A.V. Gheorghe: Decision Processes in Dynamic Probabilistic Systems. 1990,372 pp. ISBN 0-7923-0544-2

V.L. Girko: Theory of Random Determinants. 1990, 702 pp. ISBN 0-7923-0233-8

S. Albeverio, PH. Blanchard and L. Streit: Stochastic Processes and their Applica­tions in Mathematics and Physics. 1990,416 pp. ISBN 0-9023-0894-8

B.L. Rozovskii: Stochastic Evolution Systems. Linear Theory and Applications to Non-linear Filtering. 1990,330 pp. ISBN 0-7923-0037-8

A.D. Wentzell: Limit Theorems on Large Deviations for Markov Stochastic Process. 1990, 192 pp. ISBN 0-7923-0143-9

K. Sobczyk: Stochastic Differential Equations. Applications in Physics, Engineer­ing and Mechanics. 1991,410 pp. ISBN 0-7923-0339-3

G. Dallaglio, S. Kotz and G. Salinetti: Distributions with Given Marginals. 1991, 300 pp. ISBN 0-7923-1156-6

A.V. Skorohod: Random Processes with Independent Increments. 1991,280 pp. ISBN 0-7923-0340-7

L. Saulis and V.A. Statulevicius: Limit Theorems for Large Deviations. 1991,232 pp. ISBN 0-7923-1475-1

A.N. Shiryaev (ed.): Selected Works of A.N. Kolmogorov, Vol. 2: Probability Theory and Mathematical Statistics. 1992,598 pp. ISBN 90-277-2795-X

Yu.1. Neimark and P.S. Landa: Stochastic and Chaotic Oscillations. 1992,502 pp. ISBN 0-7923-1530-8

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Lin Zhengyan and Lu Zhuarong: Strong Limit Theorems. 1992, 200 pp. ISBN 0-7923-1798-0

J. Galambos and I. Katai (eds.): Probability Theory and Applications. 1992, 350 pp. ISBN 0-7923-1922-2

N. Bellomo, Z. Brzezniak and L.M. de Socio: Nonlinear Stochastic Evolution Problems in Applied Sciences. 1992, 220 pp. ISBN 0-7923-2042-5

A.K. Gupta and T. Varga: Elliptically Contoured Models in Statistics. 1993, 328 pp. ISBN 0-7923-2115-4

B.E. Brodsky and B.S. Darkhovsky: Nonparametrie Methods in Change-Point Problems. 1993,210 pp. ISBN 0-7923-2122-7

V.G. Voinov and M.S. Nikulin: Unbiased Estimators and Their Applications. Volume 1: Univariate Case. 1993,522 pp. ISBN 0-7923-2382-3

V.S. Koroljuk and Yu.V. Borovskich: Theory oJU-Statistics. 1993,552 pp. ISBN 0-7923-2608-3

A.P. Godbole and S.G. Papastavridis (eds.): Runs and Patterns in Probability: Selected Papers: 1994,358 pp. ISBN 0-7923-2834-5

Yu. Kutoyants: Identification oJ Dynamical Systems with Small Noise. 1994, 298 pp. ISBN 0-7923-3053-6

M.A. Lifshits: Gaussian Random Functions. 1995,346 pp. ISBN 0-7923-3385-3

M.M. Rao: Stochastic Processes: General Theory. 1995,635 pp. ISBN 0-7923-3725-5