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Mishura Y.S. — Stochastic Calculus for Fractional Brownian Motion and Related Processes |
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Предметный указатель |
-condition 287
(g)-transformable 61
Arbitrage 302
Arbitrage opportunity 306
Asymptotic efficiency 359
b-self-similar 7
Backward integral 161
Besov space 73 128
Bessel function of the first kind 64
Black — Scholes equation 322
Black — Scholes equation, fractional 326
Bracket 205
Burkholder — Davis — Gundy inequalities 47
C-function 287
Capital 305
Chain rule for stochastic derivative 145
Complex alternative 328
Complex hypothesis 328
Composition formulas for fractional integrals 2
Conditionally Gaussian pair 296
Confidence level 330
Convolution 59
Critical areas 330
Critical values 330
Density process 66
Derivative operator 160
Directional derivative 145
Discounted gain 305
Divergence operator 161
Dudley integral 42
Entropy maximal estimates 41
Errors of the first and of the second kind 330
Field with independent increments 119
Fractional analog of the Burgers equation 321
Fractional Brownian motion 7
Fractional Brownian motion, approximation 71
Fractional Brownian motion, backward 11
Fractional Brownian motion, forward 11
Fractional Brownian motion, geometric 302
Fractional Brownian motion, Mandelbrot — van Ness representation 9 23
Fractional Brownian motion, multi-parameter 117
Fractional derivative, Marchaud 3
Fractional derivative, Marchaud, two-parameter 119
Fractional derivative, Riemann — Liouville 2
Fractional derivative, Riemann — Liouville, two-parameter 119
Fractional derivative, Weyl representation 3
Fractional Doleans exponent 191
Fractional noise 15
Fractional Wick exponent 256
Fundamental martingale 27
Gaussian subspaces 59
Generalized Lebesgue — Stieltjes integral 123
Generalized quadratic variation 205
Girsanov theorem 67
Goodness-of-fit test 335
Hardy — Littlewood theorem 1
Hellinger process 70
Hermite functions 12
Hermite polynomials 12
Holder continuous functions 2
Hurst effect 301
Hurst law 301
Hurst phenomenon 301
Integration-by-parts formula for fractional derivatives 4
Integration-by-parts formula for fractional integrals 2
Ito formula 182
Ito formula for 185
Ito formula for fractional fields 186
Ito formula for Wick integrands 184
Lenglart inequality 48
Levy theorem 27 94
Likelihood ratio 329
Local asymptotic normality 358
Local martingale 66
Local solution 205
Long memory 59
| Long-memory Gaussian processes 59
Long-range dependence 8
Markov-type strategy 306
Martingale 27
Maximum likelihood estimate 345
Metric -capacity 41
Metric -entropy 42
Mittag — Leffler function 351
Mixed version of the Black — Merton — Scholes model 305
Modulus of continuity 87
Modulus of uniform continuity 87
Molchan martingale 27
Observation process 291
Observed trajectory 328
Optimal filter 291
Optimal filtering problem 292
Orlicz space 280
Portfolio 305
Quasi-likelihood ratio 331
Random walk 80
Rate of convergence of Euler approximations 243
Regularly varying 91
Rescaled adjusted range statistic or R/S-statistic 301
Riemann — Liouville fractional integral on 1
Riemann — Liouville fractional integral on (a, b) 1
Riemann — Liouville fractional integral, two-parameter 118
Self-financing strategy 305 306
Semi-metric 41
Semi-norm 163
Semimartingale 65 71
Signal process 291
Skorohod integral 158 161
Skorohod space 80
Skorohod topology 81
Slowly varying at oo 80
Smooth functionals 146
Sobolev space 38
Sobolev — Slobodeckij space 205
Spectral density function 8
Spectral representation 8
Stochastic derivative 145
Stochastic differential equation, Euler approximations 243
Stochastic differential equation, mixed 225
Stochastic differential equation, moment estimates for solution 56
Stochastic differential equation, pathwise 197
Stochastic differential equation, quasilinear of Skorohod type 255
Stochastic differential equation, weak solution 263
Stochastic differential equation, with additive Wiener integral 262
Stochastic differential equation, with fractional white noise 241
Stochastic Fubini theorem 57 174
Stochastic integral, generalized forward 205
Stochastic integral, generalized of kth order 168
Stochastic integral, generalized, of first order 166
Stochastic integral, Skorohod 158 161
Stochastic integral, Stratonovich 146
Stochastic integral, symmetric Stratonovich 161
Stochastic integral, w.r.t. fBm, , Wick 144
Stochastic integral, w.r.t. fBm, , Wiener 16
Stochastic integral, w.r.t. fBm, forward 161
Stopping time 46
Stratonovich integral 146
Stratonovich integral, symmetric 161
Strong martingale 120
Strong Molchan martingale 121
Testing procedure 330
The Fourier transform 5
Two-parameter left Riemann — Stieltjes integral 135
Two-sided Wiener process 9
Uniform modulus 87
Weak solution 263
Weierstrass — Mandelbrot process 79
White noise 10
Wick products 141
Wiener field 120
Wiener integral, generalized 165
Wiener integral, w.r.t. fBm 16
Wiener integral, w.r.t. fBm, moment inequalities 35
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