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| Dembo A., Zeitouni O. — Large deviations techniques and applications |
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| Предметный указатель |
 -topology 239
 -rate function 6
-smoothed rate function 283
 -topology 145 311
 -field 5 165 228 314
-field, cylinder 239 288 292
 -topology 236 239 246 260 264 278 288 292
Absolutely continuous functions 152 160 165 177
Absolutely continuous measures 314
Additive functional of Markov chain see "Markov additive
Additive set function 165
Affine regularization 135
Algebraic dual 145—149 239 246 310
Alphabet 11 58 72 84
Approximate derivative 165
Arzela — Ascoli, theorem 158 316
Asymptotic expansion 99
Azencott 150 224
Bahadur 99 150 277
Baldi's theorem 139 244
Ball 308
Banach space 55 130 142 223 229 244 292 312
Bandwidth 217
Base of topology 106-110 248—251 255 307
Bayes 77 78
Berry — Esseen expansion 96 97
Bessel process 216
Bijection 111 308
Birkhoff's Ergodic Theorem 88
Borel -field 5 102 165 237 274 314 318
Borel probability measures 144 151 228 247 281
Borel — Cantelli lemma 57 70
Bounded variation 165
Branching process 280
Bronsted — Rockafellar, theorem 142
Brownian motion 43 151 160—164 170 183 186 187—217 224 321
Brownian sheet 164—169 168
Bryc's theorem 124—129 253
Cauchy sequence 245 311
Central Limit Theorem (CLT) 34 96
Change of measure 33 53 223 236 278 293
Change point 151
Characteristic boundary 199—201 224
Chebycheff's bound see "Inequalities Chebycheff"
Chernoff's bound 78
Closed set 307
Code 86—93
Coding gain 87
Compact set 7 8 38 73 127 131 308 309
Complete space 311
Concave function 42 133
Contraction principle 20 110 144 150 154 187
Contraction principle, approximate 117 150
Contraction principle, inverse 111 150
Controllability 199
Convergence 308
Convergence determining 298 320
Convex analysis 46 139 150 305—307
Convex hull 72 228 310
Countably additive 165
Covariance 94 168
Covering 308
Cramer's theorem 2 18—20 26—42 45 55 57 69 94 113 223 227—236 277
Cumulant generating function 26
CUSUM 225
Dawson — Gaertner, theorem 144 156 275
Decision test see "Test"
Desire Andre see "Reflection principle"
Diffusion process 187—188
Digital communication 46 53 169 225
Distortion 86 87 91
Divergence 238
DMPSK 169—175 224
DNA sequences 68 151
Doeeblin recurrence 279
Domain 4
Dominated convergence 317
Donsker 9 150
Doob 193 321
Duality lemma 134—138 240 306
Dynamical systems 151 200 280
Eberlein — Smulian, theorem 242 312
Effective domain 4
Elliptic 213
Ellis 9 303 see
Empirical mean 26 68 229
Empirical measure 3 12 21 64 81 236—303
Energy 74 291
Ensemble 90 291
entropy 13 92
Epigraph 139
Equicontinuous 169 316 320
Equilibrium point 196
Equivalent measures 76 314
Ergodic 61 87 88 92 260
Error probability 54 57 76 82 171 281—283
Essentially smooth 44 47 52 147 245 306
Euler — Lagrange 175
Exchangeable 74 85 291
Exit from a domain 196—213 224
Exponentially equivalent 114 151 153 166
Exponentially good approximations 115 117 119 175 189
Exponentially tight 8 39 49 106 111 123 127 136 139 148 150 229 236—237 251 286
Exposed hyperplane 44 50 139
Exposed point 44 50 139
Fatou's lemma 35 51 156 167 230 317
Feller continuous 267—268 279
Fenchel — Legendre transform 26 42 52 101 134—138 152 155 164 212 228 244 254 263—265
Field 165 280 314
Freidlin 3 9 187—195 222
Gaertner — Ellis, theorem 43 45—54 57 94 124 130 139—143 155 227 305
Gateaux differentiable 142 148 241
Gaussian process 53 164 168 280 303
Generator 119
Gibbs 3 57 72—75 280 291—302
Gibbs, measure 295 297 299
Gibbs, parameter 74
Girsanov 223
Green's function 198 213
Gronwall's lemma 188 191 193 208 210 221 322
Hahn — Banach theorem 137 306 310
Hahn's theorem 315
Hamilton — Jacobi 212
Hamiltonian 299
Hoeffding 81 83
Hoelder continuous 164
Homeomorphism 308
Hypercontractive 263 279
Hypermixing see "Mixing"
Hypothesis testing 57 75—85 281—287 303
I continuity set 5
Inequalities, Azuma 36 55
Inequalities, Borell 164 169 235
Inequalities, Burkholder — Davis — Gundy 210 321
Inequalities, Cauchy — Schwartz 173 190
Inequalities, Chebycheff 30 33 36 38 42 45 49 132 133 141 158 163 193 205 238 244 267 300
Inequalities, Fernique 223
Inequalities, Hoeffding 35
Inequalities, Hoelder 28 37 263
Inequalities, isoperimetric 223
Inequalities, Jensen 13 19 28 40 78 93 178 240 241 243 262 268 293
Inequalities, Logarithmic Sobolev 279
Initial conditions 191 249 251
Initial measure 267
integral 314
Interacting particles 294 298 303
Interior 307
Invariant measure 265 269 270
Ioffe 306
Irreducible 58 60 63 65 71 250
| Ito 193 321
k-scan process 67
Kofman 53
Kolmogorov's extension 274 276
Kullback — Leibler distance 238 278
Lanford 277 303
Langevin's equation 213
Laplace's method 120 150 277
Large deviation principle (LDP) 5—9
Large Deviation Principle (LDP) for Banach space 244 277
Large Deviation Principle (LDP) for continuous time Markov processes 119 246—247
Large Deviation Principle (LDP) for diffusion processes 187—195
Large Deviation Principle (LDP) for empirical mean 2 45 150
Large Deviation Principle (LDP) for empirical measure 3 16 61 68 237—239 278
Large Deviation Principle (LDP) for empirical process 273—277 275
Large Deviation Principle (LDP) for i.i.d. empirical sum 2 18 27 37 228
Large Deviation Principle (LDP) for Markov chains 2 58—68 60 246—253
Large Deviation Principle (LDP) for Markov occupation time 264—269
Large Deviation Principle (LDP) for multivariate random walk 164 165—169
Large Deviation Principle (LDP) for projective limits 143—149
Large Deviation Principle (LDP) for random walk 152—160
Large Deviation Principle (LDP) for sampling without replacement 23 289
Large Deviation Principle (LDP) for topological vector spaces 130—143
Large Deviation Principle (LDP), behavior under transformations 104 110—120
Large Deviation Principle (LDP), existence 106
Large Deviation Principle (LDP), uniqueness 103
Large exceedances 176—187 225
Lattice law 95—96
Law of Large Numbers 20 40 45 50 79 227
Lebesgue measure 165 168 252
Lebesgue's theorem 156 317
Level sets 37 122 144
Levy metric 237 243 247 319
Levy process 197 201
Likelihood ratio 76 81 176 281—282
Lipschitz continuous function 160 187—189 195—196 210 215 217 255 305
Log-likelihood ratio 76
Logarithmic moment generating function 26 40 44 69 88 95 130 228 230 265 277
Lower bound 6 7 39 45 84 125
Lower semicontinuous 4 42 103 121 308
Markov see "LDP for Markov chain"
Markov additive functional 59 95 278
Markov chain 57 60 71 150 252 269 278
Markov kernel 269
Markov process, continuous time 119 151
Markov semigroup 9 261
Martingale 193 210 321
Maximal length segments 68
Mazur's theorem 229 313
Mean, of a Banach space valued variable 245
Measurable function 314
Measure space 314
Metric entropy 133 243—244
Metric space 4 9 102
Micro-canonical 291
Min-max theorem 42 133 181 186
Mixing 235 253—263 279 280
Mixing,  -mixing 254 261
Mixing, hypermixing 261 263 264 267 279
Mogulskii 3 152 166 179
Monotone class theorem 268
Monotone convergence 317
Multi-index 164
Mutual information 87
Neighborhood 307
Neyman — Pearson 76—81 98 281—282
Noise 170 201
Non-coherent detection 46 53
Norm 311
Occupation time 264—269 277
Open set 307
Partially ordered set 143 309
Partition function 295 298
Peres 259 302
Perron — Frobenius 58 62
Phase Lock Loop 212 224
Pinsker 276 290
Pointwise convergence 144 153 156 166 268 289 306
Poisson process 163 197
Polish space see "Topological Polish
Polygonal approximation and interpolation 153 166 184 220
Portmanteau theorem 238 274 320
Pre-compact set 105 133 164 285 308 316
Pre-exponent 57
Probability of error see "Error probability"
Process level LDP 273—277
Product measure 57 75 91 93 113 228 292
Product topology 229 232 309
Prohorov's criterion 150 319
Projective limit 143—149 150 155 166 236 241 274 279 309
Projective topology 143—149 156 274 277 288 309
PuLSE 217—218
Quadrature noise 53
Quadrature signal 53 170
Quasi-potential 178 198 213
Queueing 201 225
Radar 213 218
Radon — Nikodym 92 163 165 238 293 299 316
Random variables, Bernoulli 35 73
Random variables, exponential 35 46 98 160
Random variables, Geometric 98
Random variables, Normal 2 35 40 46 52 94 113 161 183 186 217 219 262
Random variables, Poisson 35 163
Random walk 68 152—160
Random walk, multivariate 164—169
Range gate 218—219
Rate distortion 86—93 87 91
Rate function 4 7
Rate function, convex 27 37 109 131 148 229 237—243 254
Rate function, good 4 34 37 104 117 142 144 229 237—243 254 268 270
Refinements of LDP 94 225
Refinements of LDP of Bahadur and Rao 95 99
Reflection principle 163 321
Regular conditional probability distribution (r.c.p.d.) 272 318
Regular measure 315 319
Relative entropy 13 62 65 80 236 238 278
Relative interior 47 305
Relative topology 308
Right filtering set 143 309
Rockafellar's lemma 47 53
Ruelle 277 303
Sample path 150
Sampling without replacement 20—25 74 85 288—291
Sanov's theorem 12 16 18 36 41 61—64 73 83 227 236—246 277 287 293
Schilder's theorem 161 163 172 188 190 223 235
Separating space, set 310
Separating,  -separated 261
Separating, well-separating 126
Sequentially compact 242 309
Set function 313
Set function, Additive, Countably additive 314
Shannon's Theorem 57 88
Shift invariant 65 271 275
Shrinks nicely 167 317
signal 53 169
Signal-to-noise ratio 53
Source coding 57 91
Spectral radius 57 63 67
Stationary 61 253 260 265
Statistical mechanics see "Gibbs"
Steep 44 52 229 307
Stein's lemma 79
Stirling's approximation 14 22 55
Stochastic differential equation 187
Stochastic matrix 58
Strassen 223
Strictly convex 35
Strong solutions 322
Strong topology 307 see
Sub-additivity 37 93 150 227 231—232 235 246—253 257 277
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