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Marcus M., Rosen J. — Markov Processes, Gaussian Processes and Local Times |
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Предметный указатель |
Abelian group 235
Adler, R.J. 241
Ahlfors, L. 142
Analytic set 583
Approximate -function 8
Approximate identity 8
Associated Gaussian process 76 324 396 398 551
Associated process 76 194 398
Associated process, family of 396
Asymptotic functions 8
Augmented filtration 67
Babkov, S. 242
Bakry, D. 242
Banach — Mazur theorem 591
Banuelos, R. 527
Bapat, R.B. 6 579
Barlow, M. 2 120 455
Bass, R.F. 5 59 526
Belyaev dichotomy 213
Belyaev, Yu. K. 213 241
Berman, N. 579
Bertoin, J. 142 188 527
Bessel process 158 581
Bessel process, squared 581
Biane, P. 61 550
Billingsley, P. 592
Bingham, N. 304 438 594
Blackburn, R. 527
Blumenthal Zero–One Law 26
Blumenthal, R. 61 119 120
Boas's Lemma 597
Boas, R. 349
Bochner integral 587
Bochner's theorem 236
Borel right process 67
Borel right process, local 179 551
Borel semigroup 63
Borell, C. 214 241
Borell, Sudakov — Tsirelson Theorem 214
Botts, T.A. 210
Bounded discontinuity 208
Boylan, E. 120
Branch point 170
Brownian motion 11 13 276
Brownian motion, canonical version 15
Brownian motion, killed 157
Brownian motion, local time of 31
Brownian motion, most visited sites of 510
Brownian motion, planar 534
Brownian motion, quadratic variation of 457
Brownian motion, two dimensional 534
Brydges, D. 1
Caballero, R. 527
CAF see continuous additive functional
Cameron — Martin formula 516
Canonical gaussian measure 193
Canonical stable process 141
Category (1) 326
Cemetery state 63
Chapman — Kolmogorov equation 12 13 77
Characteristic function 189
Chung, K.L. 61 119 361 455
Class G 326
Class S 208
Comparable functions 8
Concentration inequality 224
Continuous additive functional 32 43 83
Continuous additive functional, potential of 90
Continuous additive functional, potential operator of 90
Contraction property 125
Contraction resolvent 125 126
Contraction resolvent, strongly continuous 587
Contraction semigroup, strongly continuous 122 588
Counting measure 184
Covariance kernel 203
Cylinder sets 20 398
De la Vega, F. 495
Death time 72
Dellacherie, C. 73 119 180 188
Den Hollander, F. 60
Diameter of a metric space 244
Diffusion 144 530
Distinguishable set 233
Donoghue, W. 236
Donsker, M. 527
Doob's inequality 86 101
Doob, J.L. 101 237
Dudley's metric entropy condition 238 245 249 251
Dudley, R.M. 4 5 215 238 244 245 280 456 495
Dyadic numbers 580
Dynkin Isomorphism Theorem 364 380
Dynkin, E.B. 394
Edwards model of polymers 60
Ehrhard, A. 241
Eisenbaum Isomorphism Theorem 362 383 454
Eisenbaum, N. 1 2 5 6 60 61 527 534 550 579
Erdoes, P. 361
Excessive function 182
Excessive regularization 165
Exponential random variable 202
Favorite point 497 see
Feller process 121
Feller semigroup 121
Feller, W. 91 141 166 382 566 594 596
Fernique's Lemma 238
Fernique, X. 4 238 241 242 251 280 361
Filtered 7
Filtration 6
First hitting time 24 70 151
Fitzsimmons, P. 61 120 188
Fourier transform 9
Fractional Brownian motion 276
Fractional Brownian motion, scaling property 498
Froehlich, J. 1
Fukushima, M. 119
Garcia, A.M. 280 361
Gaussian lacunary series 336
Gaussian Markov process 195
Gaussian metric 233
Gaussian process 193
Gaussian process with infinitely divisible squares 561
Gaussian process, associated 76 194 270 398
Gaussian process, Banach space–valued 225
Gaussian process, boundedness 255 263
Gaussian process, class G 326
Gaussian process, continuity 255 267
Gaussian process, covariance kernel of 193
Gaussian process, mean function of 193
Gaussian process, metric for 233
Gaussian process, modulus of continuity for 258
Gaussian process, p-variation of 457
Gaussian process, periodic 280
Gaussian random variable 189
Gaussian random variable with infinitely divisible squares 560
Gaussian random variable, characteristic function of 189
Gaussian random variable, covariance matrix of 189
Gaussian random variable, mean vector of 189
Gaussian sequence 193
Generalized Second Ray — Knight Theorem 455
Generator 556
Getoor, R. 61 119 120 188
Goldie, C. 304 438 594
Griffin, P. 59 526
Griffiths, R.C. 6 579
Group 235
h-transform 109 112
h-transform process 112
Hawkes, J. 2 120 455
Hille — Yosida theorem 587
Hitting time, first 24 70 151
| Hitting time, measurability of 70
Horn, R.A. 579
Hu, Y. 60
Hunt process 120 152
Hunt's Theorem 127
Ibragamov, I. 142
Increments variance 307 317
Infinitely divisible process 135
Infinitely divisible squares 560
Inverse local time 39 97
Inverse local time of a symmetric stable process 502
Inverse time 105
Irreducible matrix 600
Isomorphism theorems 49
Isoperimetric inequality 214
Ito, K. 58 213 241 593
Jain, N. 213 241 242 280 593
Johnson, C.R. 579
Kac's Moment Formula 44 49 116 117
Kac, M. 61
Kahane, J.-P. 229
Kallenberg, O. 188
Kallianpur, G. 213 241
Karamata, J. 594
Karhunen — Loeve expansion 206
Kaspi, H. 2 6 61 395 579
Katzenelson, Y. 336
Kawada, T 495
Kesten, H. 120
Khintchine's law of the iterated logarithm 15 431
Khoshnevisan, D. 188 527
Killed process 81 152
Killing operator 110
Knight, F. 49 58 61
Kolmogorov Construction Theorem 14 122 173
Kolmogorov's Theorem for path continuity 580
Kolmogorov, A.N. 243 441 455
Konig, W. 60
Kono, N. 361 495
Lacey, M. 527
Lacunary series 336
Landau, H.J. 242
Laplace transform 565
Law of the iterated logarithm 15 470
Le Jan, Y. 119
Ledoux, M. 4 241 242 280 591
Left continuous inverse 270
Left-hand limit 8 147
Levy exponent 135
Levy measure 330
Levy process 135 212
Levy process without a Gaussian component 139
Levy — Ito — Nisio Theorem 591
Levy — Khintchine Theorem 136
Levy's inequality 591
Levy's uniform modulus of continuity 15
Levy, P. 61 456
Li, W. 242
Lifshits, M.A. 241
Linnik, Y. 142
Local of a Markov process 98
Local time 62 83
Local time, Brownian 31
Local time, continuity of 410
Local time, inverse 39 93
Local time, joint continuity 98
Local time, jointly continuous 32 58 99
Local time, modulus of continuity for 59
Local time, moment generating function of 115
Local time, normalization of 92
Local time, p-variation of 479
Local time, quadratic variation of 59
Local time, stochastic integral representation 56
Local time, total accumulated 56 99
Local uniform continuity 9
Local uniform convergence 9
Locally homogeneous 421
Locally homogeneous metric space 359
Lusin's theorem 585
Maisonneuve, B. 119
Majorant 274 297
Majorizing measure 256
Marcus, M.B. 1 2 5 61 120 188 241 242 280 361 454 455 457 495 527 579 593
Markov kernel 62
Markov process 62
Markov process, Gaussian 195
Markov process, right continuous simple 64
Markov process, simple 63
Markov process, standard 151
Markov property 19 62
Markov property, local strong 182
Markov property, simple 20 21 64
Markov property, strong 24 67
Markov semigroup 63
McKean, H. 58 120
McShane, E.J. 210
Measurable space 6
Median 7
mesh 456
Metric entropy 244 271
Meyer, P.-A. 73 119 120 180
Millar, P.W. 120
Minorant 274
Modulus of continuity 15
Modulus of continuity for a Gaussian process 258
Modulus of continuity, exact local 282
Modulus of continuity, exact uniform 282
Modulus of continuity, m- 292
Molchan, G. 5 527
Moment generating function 115
Monotone Density Theorem 595
Most visited sites 59 497 510
M–matrix 561 601
Negative 6
Negative off-diagonal elements 552
Nisio, M. 213 241 361 593
Non-decreasing rearrangement 271
Normal random variable 192
Normalized regularly varying function 304
Occupation density formula 99
Occupation measure 33
Operator norm 457
Optional -algebra 174
Optional process 175
Optional set 175
Ornstein — Uhlenbeck process 57
Oscillation function 209
Oshima, Y. 119
p-variation 457
Packing number 244
Paley — Zygmund Lemma 597
Parseval's theorem 10
Partition 456 458
Pathwise connected space 567
Perkins, E. 59 496
Permutation matrix 600
Pisier, G. 241 280 281
Pitman, E.J.G. 594
Pitman, J. 61 120
Plemmons, R.J. 579
Port, S.C. 61
Positive 6
Positive definite 76 78
Positive definite function 190
Positive definite matrix 190
Positive matrix 552 561
Positive maximum principle 127
Positive operator 122 127
Positive row sums 552
Potential 183
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