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Chung K.L., Walsh J.B. — Markov Processes, Brownian Motion, and Time Symmetry
Chung K.L., Walsh J.B. — Markov Processes, Brownian Motion, and Time Symmetry



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Название: Markov Processes, Brownian Motion, and Time Symmetry

Авторы: Chung K.L., Walsh J.B.

Аннотация:

This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zurich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2005

Количество страниц: 432

Добавлена в каталог: 04.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$B^-$      355
$B_d$      254
$L_A^-$      311
$S_A$      240 357 361 377 385
$\mathfrak{B}$      401
$\mathfrak{B}_{min}$      403
$\mathscr{E}$      1
$\mathscr{E}^{\cdot}$      96
$\mathscr{E}^{\tilde}$      63
$\mathscr{F}^{\mu}_T$      61
$\mathscr{F}_t$, $\mathscr{F} (= \mathscr{F}_{\infty})$      16 75
$\mathscr{F}_T$, $\mathscr{F}_{T+}$      14
$\mathscr{F}_T'$      57
$\mathscr{F}_t^{\circ}$, $\mathscr{F}^{\circ}_t (= \mathscr{F}^{\circ}_{\infty})$, $\mathscr{F}_t'$      2
$\mathscr{f}_{T-}$      62
$\pi_A$      237
Absorbing state      9
Additive functional      199
Almost sure(ly)      26 51
Analytic set      40
Approximation of entrance and hitting times      93 94 113
Area of sphere      150
Augmentation      29 59
Austin, D.      302
Balayage      98 375
Barrier      179
Birth time      337
Blumenthal's zero-or-one law      64
Borel measurable process      18
Borelian semigroup      46
Boundary point      246
Boundary value problem for Laplace equation      see under "Dirichlet problem"
Boundary value problem for Schroedinger equation      204
Branching measure      355
Branching point      246 254 259 280 321 348 355
Branching point, degenerate      254 274
Branching point, fork      255
Brownian motion      11 118 125 128 144ff 228 247 410
Brownian motion, continuity of paths      78
Brownian motion, killed outside a domain      177
Brownian motion, polarity of singleton      118 169
Brownian motion, potential density      128 129
Brownian motion, recurrence, transience      145
Brownian motion, rotational symmetry      149
Brownian motion, stopped      188
Brownian motion, transition density      144
Canonical space      321 324
Capacitable      388
Capacity      223 228 394
Capacity, Choquet      396
Cartan's theorem      116
Choquet's capacibility theorem      91
Choquet, G.      415
Chung, K.L.      298 302 415
Co-branching point      348
Co-capacity      394
Co-excessive      344 363
Co-left-regular      364
Co-optional      330
Co-polar      361 389
Co-potential      369
Co-semi-polar      361
Co-terminal time      338 360
Co-terminal time, associated      339
Cofine component      370
Cofine continuity      391
Cofine topology      390
Compactification      248
Compatible      281
Cone condition      165
Continuity of paths      77
Continuity principle      231
Continuity, cofine      391 392
Continuity, fine      370 390 391
Convolution semigroup      137
Death time      337
Debut      40
Debut after t      267
Dellacherie's theorem      113
Dirichlet problem      166 286 287 411
Dirichlet problem for unbounded domain      170
Dirichlet problem, generalized      170 186
Dirichlet problem, unsolvable      167
Divergence formula      157
Domination principle      100
Doob — Meyer decomposition      48
Doob's continuity theorem      184 189
Doob's stopping theorem      30
Doob, J.L.      243 302 334 414
Double reversal      337 339
Dual process      139
Dual transition function      309
Duality      344 347
Duality formula      140
Duality, weak      344
Dynkin's lemma      4
Electrostatics      229 377
Energy      224
Energy minimization      226 230
Energy minimization principle      225
Entrance law      265
Equilibrium measure      213 3
Equilibrium measure as steady state      227
Equilibrium potential      384
Equilibrium principle      218
Essential inf      233
Essential limit      233 242 271 293 294 311 312
Essential limit point      296
Essential separability      235 266
Essential sup      233
Essential topology      233 242
Exact      339
Excessive function      45 85
Excessive function as limit of potentials      82 85 86
Excessive function, balayage properties      100
Excessive function, closure properties      81 104
Excessive function, decreasing limit      116ff
Excessive function, fine continuity      108
Excessive function, infinity of      104
Excessive function, purely      121
Excessive function, right continuity on paths      101
Excessive measure      349 350
Excessive minimal      327 330 331
Excessive regular      386 391
Excursion      153
Feller process      50 289
Feller property      49 251 261
Feller property, strong      129 372
Feller — McKean diffusion      300
Feller, W.      248
Feynman — Kac functional      199
Filtration, continuity      259
Fine closure      97
Fine component      370 376
Fine continuity      370 390 391
Fine limit      413
Fine neighborhood      413
Fine recurrence      416
Fine symmetry      388
Fine topology      107 390
Fine transience      416
First blow-up      245
First entrance time      22
First entrance time, optionality, approximation      see under "hitting time"
First infinity      245
Fork      255 279
Frostman      230
Functional, additive      358
Functional, multiplicative      358
Gauge      205
Gauss formulas      157 162
Gauss formulas, quadratic      232
Gauss — Koebe theorem      156
Generalized Dirichlet problem      186
Getoor, R.      341
Ghostly return      298
Green's function      410
Green's function, potential      181
Green's function, potential, for an interval      199
h-excessive      322 323 328 332 377
h-excessive measure      366
h-polar      332
h-thin      329 330
h-transform      325 331 332 334 348 364 365 367 376 378 396
h-transform, semigroup      321
Harmonic function      156ff 287 379 412
Harmonic function and martingale      182
Harmonic measure      162 412
Harnack's theorems      158
Harnack's theorems, inequality      200
Hitting probabilities for spheres      168 169
Hitting time      70
Hitting time, approximation      93 94 113
Hitting time, optionality      71 92
Hoelder condition      162
Holding point      79
Holes      342
Homogeneity      6
Homogeneity, spatial      137
Hunt process      75ff 244 245 258 276 277 288
Hunt's Lemma      238 280 313
Hunt's switching formula      219
Hunt, G.A.      384 397 414
Hypothesis, $(\hat{SF})$      371 374 375 378 386 387 389 391
Hypothesis, (B)      131 212 357 378 385—387 396
Hypothesis, (L)      112 347 354 361 385 416 419
Hypothesis, (MMP)      272 273 280
Hypothesis, (MP)      269 270
Hypothesis, (SF)      389 391
Hypothesis, (SMP)      272 273 280
Hypothesis, (UH)      274
Independent increments      142
inf-stable      269
Initial distribution      7
Instantaneous state      56
Invariant field      327 408
Invariant function      121
Invariant function, measure      138
Jacobsen, M.      341
Jump chain      245
Kellogg — Evans theorem      185 223
Kernel      6
Killing      279
Killing operator      353
Knight's Lemma      270 290
Knight, F.      268 290
Kolmogorov's extension theorem      6
Kunita, H.      290 397 414
Laplace equation      156
Laplace equation, radial solution      159
Laplacian as infinitesimal generator      190 198
Laplacian as infinitesimal generator as inverse to potential operator      192 194
Last exit      329 394
Last exit time      121 209
Lazy crotch      286 289
Lcrl      272
Left co-polar      361
Left continuity      240
Left entrance, hitting time      95 134
Left polar      361
Left quitting time      213
Left-branching point      355
Left-regular      279 361
Levy process      137
Lifetime      9
Logarithmic potential      193
Maria — Frostman      221
Markov chain      10 244 291
Markov process      2
Martin boundary      347 401 410 414
Martin compactification      409
Martin kernel      399 401 410
Martin representation      404 406
Martin space      399 401 410
Martin, R.S.      398 414
Martingale      24 259
Martingale for Brownian motion      147 153
Maximum principle      394 see
Maximum principle for harmonic function      158
McKean, H.P.      300
Measurability questions      63
Meyer's theorem      32
Meyer, P.-A.      251 341 415
Minimal chain      245
Minimal function      327 328 403 411
Minimal point      403 410
Moderate Markov property      69 256 298 303 354
Mokobodzki, G.      318 356 415
Monotone class      4
Near symmetry      393
Nearly Borel      95
Nearly equivalent      391
Occupation time      109
OPTIONAL      12
Optional field      43
Optionality of entrance and hitting times      71 92
p-potential      369
Penetration time      237 284 293
Penetration time, other      361
Perfect      339
Picard's theorem      161
Pitman, J.W.      341
Pittenger, A.O.      341
Point at infinity      9 48
Poisson equation      193 194 196
Poisson formula      169
Poisson integral      180
Poisson process      11
polar      110 389
Polarity principle      222
Pole      330
Positivity principle      230
Potential      46 266 375 380 384
Potential lower semi-continuity      126
Predictable      17
Predictable field      43
Predictable time      258 289
Process, Hunt      75 244 245 258 276 277 288
Process, moderate Markov      251 255 258 273 304 354—356 365 418
Process, Poisson      11
Process, Ray      258—260 263 266 268 270 274 276 303
Process, standard      246 277 288
Process, strong Markov      255 256 268 272 273 365
Progressive measurabilify      37
Projection theorem      40
Q-matrix      244
Quasi left continuity      70
Quasi-left continuity      264 356 357 362 385—387 396
Quitting kernel      209 212 213
Quitting time      121 209 213
Radon measure      212
Ray process      258 260 263 266 268 270 274 276 293 303
Ray resolvent      251 270 303
Ray — Knight compactification      268 272 286 291 292 301 303 337 409
Ray, D.      251 290
rcll      272
Recurrent process      122
Recurrent process set      121
Reduite      327
Reduite, exterior      385
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