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| Авторизация |
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| Resnick S.I. — A probability path |
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| Предметный указатель |
Inequalities, Dubins 371
Inequalities, Holder 186 189 201
Inequalities, Jensen 188
Inequalities, Markov 130
Inequalities, Minkowski 187 201
Inequalities, modulus 128
Inequalities, Schwartz 186 187 196
Inequalities, Skorohod 209 210
Inner product 181
Integral comparison lemma 336
integrand 134
Integration 117 119
Intersection 3
Interval of continuity 248 250
Inverse 61 71
Inverse, distribution function 61 66
Inverse, map 71
Inversion formula 328
Jensen inequality 188
Kolmogorov convergence criterion 212 243 435
Kolmogorov zero-one law 107 108 217
Kronecker lemma 214
Ladder time 89
Laplace transform, inversion 239
Law of Large Numbers 1 130
Law of Large Numbers, strong 208 213 219
Law of large numbers, strong, applications 222
Law of large numbers, weak 130 176 204
Law of rare events 306 325
Lebesgue decomposition 334 382
Lebesgue decomposition, supermartingale 382
Lebesgue dominated convergence 175
Lebesgue integral 139
Lebesgue interval 158
Lebesgue measure 57 62 88 157 160
Lebesgue measure, circular 86
Lebesgue measure, dyadic expansion 88
Lebesgue — Stieltjes integral 119
Levy metric 285
Levy theorem 210—212
Liapunov condition 319 321 323 326
Limits 6
Limits, sets 6
Limits, sets, liminf 6
Limits, sets, limsup 6
Lindeberg condition 314 319 322 326 329 330 332
Lindeberg condition and Liapunov condition 319
Lindeberg — Feller CLT 314 321
Linear 123
Log-odds ratio 283
m-dependence 236 270
Market model 416
Markov inequality 130
Martingale 2 333 353
Martingale difference 354
Martingale difference, orthogonality 355
Martingale,  -bounded 390 396
Martingale, arbitrage 420
Martingale, closed 374
Martingale, closed, examples 374
Martingale, closure 373
Martingale, complete market 426
Martingale, convergence 387
Martingale, convergence theorem 2
Martingale, definition 353
Martingale, differentiation 382
Martingale, Doob decomposition 360 362
Martingale, entymology 355
Martingale, examples 356
Martingale, examples, branching process 359 380
Martingale, examples, differentiation 382 385
Martingale, examples, finance 416
Martingale, examples, gambler’s ruin 379 410 411
Martingale, examples, gambling 356
Martingale, examples, generating functions 357
Martingale, examples, likelihood ratio 359
Martingale, examples, Markov chains 358
Martingale, examples, random walk 398 400 401 409
Martingale, examples, smoothing 356
Martingale, examples, sums 356
Martingale, examples, transforms 356
Martingale, finance 416
Martingale, Krickeberg decomposition 386
Martingale, mean approximation lemma 431
Martingale, optimal stopping 2
Martingale, random walk, regular 402
Martingale, regular 390
Martingale, reversed 412
Martingale, reversed, convergence 412
Martingale, reversed, examples 412
Martingale, reversed, mixing 415
Martingale, reversed, SLLN 412
Martingale, stopped 377 379 392
Martingale, stopping time, integrable 407
Martingale, stopping time, regular 402
Martingale, submartingale 360 362
Martingale, transform 356
Martingale, uniformly integrable 389
Martingale, viable market 420
Martingale, Wald identity 398
Mathematical finance 416
Mean 164
Mean approximation lemma 165 431
Mean square error 181
Mean,minimizes  prediction. 164
Measurable 74 118 144 162
Measurable map 74
Measurable space 74
Measurable, composition 77
Measurable, continuity 80
Measurable, limits 81
Measurable, test 76
Measures, absolutely continuous 334
Measures, Lebesgue decomposition 334
Measures, mutually singular 334
Median 164 201
Median, exists 164
Median, minimizes prediction 164
Metric space 65 78
mgf 294
Minimal structure 36
Minkowski inequality 187 191 201
Mixing 415
Mixing, tail  -field 415
Modulus inequality 128
Moment generating function 160 294 299
Moment generating function, central limit theorem 294
Monotone class 35
Monotone Convergence Theorem 123 131 152
Monotone convergence theorem, series version 131
Monotone function 87
Monotone sequence of events 8
Monotone sequence of events, and indicator functions 10
Monotonicity 31
Monotonicity, events 135
Monotonicity, expectation 121 127 128 134
Monotonicity, function 87
Monotonicity, measures 31
Monte Carlo method 234
Mutually singular 245
Negligible set 66
Non-atomic 64
Non-defective 248
Non-negative definite 327 328
Non-parametric estimation 178
Normal density 162 193 299
Normal random variable 112
Null set 66
Occupancy problem 234
Occupation time 153
| Option pricing 428
Order statistics 116 178 285 287
Orthonormal 331
Pairwise disjoint 3
Pareto distribution 286
Pivot 283
Point process 79
Poisson random variable 113
Polya urn 431
Portmanteau theorem 263 264
Potential 440
Power set 2
Pratt Lemma 164
Predictable 356
Prediction 164
Prediction, 164
Prediction, 164
Prediction, best linear 164
Predictor 181
Price system 441
Probability measure 29 66
Probability measure, additive 43
Probability measure, construction 57
Probability measure, construction, Lebesgue measure 57
Probability measure, construction, measure with given df 61
Probability measure, extension 43
Probability space 29
Probability space, coin tossing 41
Probability space, construction 40
Probability space, construction, discrete 41
Probability space, construction, general 43
Probability space, discrete 41
PRODUCT 145 147
Product comparison lemma 313
Product space 143
Product, -field 145
Prohorov theorem 309
Projection 335
Projection map 80 143
Proper 248
Proper convergence 249
Pure birth process 216
Quantile 178 279
Quantile estimation 178
Quantile estimation, weakly consistent 179
Radon — Nikodym derivative 333
Random element 74 78
Random function 79
Random measure 79
Random permutation 34
Random sequence 79
Random signs 234
Random variable 71 75 79 93
Random variable, Bernoulli 176
Random variable, bounded 86
Random variable, discrete 94
Random variable, exponential 105
Random variable, normal 112
Random variable, Poisson 113
Random variable, tail 107
Random variable, tail equivalent 203 204
Random vector 79
Random walk 89 398
Random walk, simple 409
Random walk, skip free 404
Rank 95
Rapid variation 163 197
Record 95 215 320
Record, counts 215 320
Record, counts, asymptotic normality 320
rectangle 144
Regular Borel set 70
Regular measure 70
Regular variation 286
Regularity 388 393
Regularity, criteria 391
Regularity, stopping 390
Relative compactness 309
Relative rank 89 96
Relative stability sums 240
Renewal theory 222 331
Renyi 96
Renyi representation 116 285
Renyi theorem 95 96 114 155
Riemann integral 139
Risk neutral measure 420
Riskless asset 416
Sample mean 247
Sample median 287
Sampling with replacement 287
Sampling without replacement 34
Scheffe lemma 190 253 284 287
Scheffe lemma and convergence 190
Schwartz inequality 186 187 196
Second continuous mapping theorem 287
Second converging together theorem 269 273
Section, function 144 146
Section, set 143 145
Selection theorem 307 309 326
Self-financing 417
Self-financing, characterization 417
Semi-continuous function 4 87
Semialgebra 35 43 66 144
Semialgebra, field generated by 45
Semialgebra, intervals 44
Semialgebra, rectangles 44
Separating hyperplane theorem 423
Set difference 3
Set operations 11
Simple function 84 117—119 136
Simple function, expectation 119
Skorohod inequality 209 210
Skorohod theorem 258 259 261 262
Slutsky theorem 268
Spacings 116 285
St. Petersburg paradox 240 241
Stationary process 181
Statistic 171
Stirling formula 323
Stirling formula, CLT proof 323
Stochastic process 88
Stopped process 88
Stopping theorems 392
Stopping time 363
Stopping time, comparison 366
Stopping time, definition 363
Stopping time, hitting time 364
Stopping time, integrable 407
Stopping time, preservation of process mean 367
Stopping time, properties 365
Stopping time, regular 392
Stopping time, regular, characterization 394
Stopping time, regular, criteria 393 394 397
Strong Law of Large Numbers 208 213 219 220
Strong law of large numbers, Kolmogorov 220
Strongly consistent 171
Structure 35
Structure, minimal 36
Subadditivity, measures 31
Submartingale 386
Subsequence criterion 172
Sums of independent random variables 209
Supermartingale 366
Supermartingale, Lebesgue decomposition 382
Supermartingale, positive 366 367
Supermartingale, positive, bounded 369
Supermartingale, positive, convergence 371 373
Supermartingale, positive, operations 367
Supermartingale, positive, pasting 367
Supermartingale, positive, stopped 368
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