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Resnick S.I. — A probability path
Resnick S.I. — A probability path

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Название: A probability path

Автор: Resnick S.I.

Аннотация:

Many probability books are written by mathematicians and have the built in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance, and engineering.


Язык: en

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 472

Добавлена в каталог: 29.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L_1$      126
$l_2$      181
$L_p$      180
$L_p$, convergence      189
$L_p$, convergence and convergence in probability      181
$L_p$, metric      180
$L_p$, norm      180
$L_{\infty}$      201
$\lambda$-System      36
$\lambda$-system, new postulates      36
$\lambda$-system, old postulates      36
$\pi$-system      36 37
$\sigma$-additive class      36
$\sigma$-algebra      13 29
$\sigma$-field      13 20 22—24
$\sigma$-field, almost trivial      108
$\sigma$-field, complete      66
$\sigma$-field, countably generated      24
$\sigma$-field, generated by a map      83
$\sigma$-field, generated by continuous functions      87
$\sigma$-field, minimal      15
$\sigma$-field, permutable      26
$\sigma$-field, product      145
$\sigma$-field, tail      107
Absolute continuity      333
Adapted process      364
Additive      43
Admissible strategy      419
Algebra      12
Almost all      167
Almost certainly      167
Almost everywhere      167
Almost sure convergence      167
Almost sure convergence and continuous maps      174
Almost sure convergence and convergence in probability      170 171
Almost sure convergence, not metrizable      200
Almost surely      167
Almost trivial $\sigma$-field      108
Arbitrage      419
Arbitrage strategy      419
Arzela — Ascoli theorem      326
Asymptotic density      26
atom      24 64
Atom, of algebra      24
Atom, of probability space      64
Autocovariance function      327
Autoregression      227
Baby Skorohod theorem      258 259 261 262
Ballot problem      439
Beppo Levi Theorem      165
Bernoulli random variable      103 163 176 285
Bernstein polynomial      176 238
Big block-little block method      271
Binomial distribution      176 282
Birth process      216
Bonferroni inequalities      30
Borel sets      16
Borel sets, comparing      18
Borel sets, extended      25
Borel sets, metric space      18
Borel sets, open sets      18
Borel sets, ways to generate      17
Borel zero-one law      103 115 219
Borel — Cantelli lemma      102 163 204
Borel — Cantelli Lemma, partial converse      236
Branching process, immigration      435
Bridge      69
Cantor distribution      244
Cauchy criterion      171
Cauchy density      126 193 286
Cauchy equation      280
Cauchy in probability      211
Central limit theorem      1 253 270 282—284 287 294 302 313
Central limit theorem, DeMoivre — Laplace      253
Central limit theorem, Liapunov condition      319
Central limit theorem, Lindeberg condition      314
Central limit theorem, Lindeberg — Feller      314
Central limit theorem, m-dependence      270
Central limit theorem, proof      312
Central value      162 201
Characteristic function      293 295
Characteristic function, bilateral exponential density      328
Characteristic function, cauchy density      328
Characteristic function, Continuity Theorem      304
Characteristic function, derivatives and moments      301
Characteristic function, elementary properties      296
Characteristic function, expansions      297
Characteristic function, exponential density      328
Characteristic function, normal density      299
Characteristic function, selection theorem      307 309
Characteristic function, triangle density      329
Characteristic function, uniform density      328
Characteristic function, uniqueness theorem      302
Chebychev inequality      130 131 176 181 185 315
CHF      295
Circular Lebesgue measure      86
Closure      11 12 35 373 374 388
Coincidences      34
Comparison lemma      141
Complement      3
Complete convergence      250
Complete market      425 441
Complete market, option pricing      441
Completion      66
Completion, $\sigma$-field      66
composition      77
Conditional expectation      2 339
Conditional expectation, countable partitions      341
Conditional expectation, definition      340
Conditional expectation, densities      344
Conditional expectation, discrete case      343
Conditional expectation, existence      340
Conditional expectation, independence      349
Conditional expectation, properties      344
Conditional expectation, properties, dominated convergence      347
Conditional expectation, properties, Fatou lemma      346
Conditional expectation, properties, Jensen inequality      351
Conditional expectation, properties, linearity      344
Conditional expectation, properties, modulus inequality      345
Conditional expectation, properties, monotone convergence      346
Conditional expectation, properties, monotonicity      345
Conditional expectation, properties, norm reducing      352
Conditional expectation, properties, product rule      347
Conditional expectation, properties, projections      349
Conditional expectation, properties, smoothing      348
Conditional expectation, Radon — Nikodym derivative      340
Conditional probability      341
Conditional variance      363
Consistency      1
containment      4
Contingent claim      425
Contingent claim, attainable      425
Continuity      31 32
Continuity theorem      304 326 330
Continuity theorem, proof      311
Continuity, measurability      80
Continuity, measures      31 32
Continuous functions      79 159
Continuous mapping theorem      261 287
Continuous mapping theorem, second      287
Continuous maps      174
Continuous paths      88
Convergence in distribution      247 251
Convergence in probability and almost sure convergence      170 171
Convergence in probability and continuous maps      174
Convergence in probability and dominated convergence      175
Convergence in probability, Cauchy criterion      171
Convergence in probability, metrizable      199
Convergence in probability, subsequence criterion      172
Convergence to types theorem      274 275 279 289 290 321 329
Convergence, $L_p$      180
Convergence, almost sure      167
Convergence, complete      250
Convergence, in distribution      247 251
Convergence, in probability      169
Convergence, proper      249
Convergence, vague      249
Convergence, weak      249 251
Converging together theorem, first      268
Converging together theorem, second      269 273
Convolution      154 293
Convolution transform      288
Coordinate map      143 162
Correlation      181
Coupon collecting      242
Covariance      128
Crystal ball condition and uniform integrability      184
de Morgan’s laws      5
Delta method      261 288
DeMoivre — Laplace central limit theorem      253
density      135 139
Density, Bernoulli      323
Density, Cauchy      126 286 288 328
Density, exponential      285 287 288 323
Density, extreme value      279
Density, gamma      160 163 285 325
Density, normal      162 163 284 287 288 299
Density, Pareto      286
Density, Poisson      288 321
Density, triangle      329
Density, uniform      286 287 289 322
Diagonalization      307
Discounted price process      416
Discrete uniform distribution      266
Distribution function      33 38 42 61 66 138 159 247
Distribution function, inverse      61 66
Distribution function, non-defective      248
Distribution function, proper      248
Distribution, measure      137
Dominated convergence      133 157 158 160 161 163 164 175
Dominated convergence and convergence in probability      175
Dominated family and uniform integrability      183
Dominating random variable      132 133
Doob decomposition      360 362
Doob martingale convergence theorem      387
Dubins’ inequality      371
Dyadic expansion      88 95 98 115
Dyadic expansion, Lebesgue measure      88
Dynkin class      36
Dynkin’s Theorem      36—38 93
Egorov theorem      90
Empirical distribution function      224
Equicontinuous sequence      326
Equivalence class      64
Equivalent events      64
Equivalent martingale measure      420 441
Equivalent martingale measure, unique      426
Estimate      171
Estimation      170 171
Estimation, quantile      178
Estimator      171 282
Estimator, strongly consistent      171
Estimator, weakly consistent      171
Euler’s constant      321
European call      425
European option      425
European put      425
Event      2 29
Event, tail      107
Exception set      167
Expectation      117 119
Expectation, basic properties      123
Expectation, extension      122
Expectation, linear      123
Expectation, simple function      119
Exponential random variable      105
Exponential tilting      403
Extended real line      25
Extension      43
Extension theorem      46 48 49
Extension theorem, combo      48
Extension theorem, first      46
Extension theorem, second      48 49
Extreme value distribution      278 279
Extreme value theory      168 197 278 286 289
Factorization criterion      94
Fair sequence      354
Fatou lemma      32 132 164 166
Fatou lemma, expectation      132 133
Fatou lemma, measures      32
Field      12 22 24 63
Finance, admissible strategy      419
Finance, arbitrage      419 420
Finance, arbitrage strategy      419
Finance, complete market      425
Finance, contingent claim      425
Finance, contingent claim, attainable      425
Finance, discounted price process      416
Finance, European call      425
Finance, European put      425
Finance, first fundamental theorem      420
Finance, market model      416
Finance, martingale      416
Finance, option pricing      428
Finance, price system      441
Finance, risk neutral measure      420
Finance, second fundamental theorem      426
Finance, trading strategy      417
Finance, viable market      420
Finite dimensional distribution functions      93
Finite dimensional distribution functions and independence      93
First category set      67
First converging together theorem      268
Fourier inversion      303 328 329
Fubini theorem      143 147
Function, monotone      87
Function, upper semi-continuous      87
Gambler’s ruin      410 411
Gamma density      160
Generating function      161
Glivenko — Cantelli lemma      284
Glivenko — Cantelli theorem      224
groupings      100
Gumbel distribution      279
Haar function      433
Hamel equation      280
Heavy tail      126
Heavy tailed time series models      227
Hedged security      425
Hilbert space      181 334
Holder inequality      186 189 201
Hypograph      4
Inclusion-exclusion formula      30 35 63 64 68 70
Inclusion-exclusion formula, coincidences      34
Increasing process      360
Independence      91 130 143 155
Independence, arbitrary number of classes      93
Independence, basic criterion      92
Independence, classes      92
Independence, groupings      100
Independence, groupings lemma      101
Independence, many events      91
Independence, random variables      93
Independence, random variables, discrete      94
Independence, random variables, factorization criterion      94
Independence, two events      91
Indicator function      5
Induced probability      75
Inequalities      186
Inequalities, Chebychev      130 131 176 181 185
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