Mishura Y.S. — Stochastic Calculus for Fractional Brownian Motion and Related Processes :: Электронная библиотека попечительского совета мехмата МГУ

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Mishura Y.S. — Stochastic Calculus for Fractional Brownian Motion and Related Processes

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Название: Stochastic Calculus for Fractional Brownian Motion and Related Processes

Автор: Mishura Y.S.

Аннотация:

The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 393

Добавлена в каталог: 10.05.2008

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Предметный указатель

$\Delta^2$ -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 $H \in (0, 1/2)$       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 $\varepsilon$ -capacity      41
Metric $\varepsilon$ -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 $\mathbb{R}$       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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