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Marcus M., Rosen J. — Markov Processes, Gaussian Processes and Local Times
Marcus M., Rosen J. — Markov Processes, Gaussian Processes and Local Times

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Название: Markov Processes, Gaussian Processes and Local Times

Авторы: Marcus M., Rosen J.

Аннотация:

Written by two foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and for experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum, then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original, readable book will appeal to both researchers and advanced graduate students.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 620

Добавлена в каталог: 19.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group      235
Adler, R.J.      241
Ahlfors, L.      142
Analytic set      583
Approximate $\delta$-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 $L_p$ 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 $\sigma$-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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