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Rößler A. — Numerical Methods for Stochastic Differential Equations
Rößler A. — Numerical Methods for Stochastic Differential Equations

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Название: Numerical Methods for Stochastic Differential Equations

Автор: Rößler A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 86

Добавлена в каталог: 01.12.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$H^{2}[0, T]$      24
$L^{2}[0, T]$      18
$\mathcal{M}^{c}$      20
$\mathcal{M}^{c}_{2}$      20
Additive noise      (see Noise)
Approximation      57
Approximation, mean-square      59 61
Approximation, moment      58
Approximation, one-step      61
Approximation, pathwise      58
Approximation, strong      58
Approximation, strong Ito — Taylor      75
Approximation, weak      58
Borel set      5 12
Box-Muller method      (see Transformation)
Brownian motion      8
Coefficient function Ito      71
Commutative noise      (see Noise)
Commutativity condition      80
Concatenation operation      72
Conditioning formula      53
Convergence, strong      58
Convergence, weak      59
Covariance matrix      52
Diagonal noise      (see Noise)
Diffusion matrix      37
Discretization      57
Distribution, normal      52
Doob’s inequality      (see Inequality)
Drift      9
Drift vector      37
Equidistant      57
Euler — Maruyama scheme      57 67 76
Event      1
Expectation, conditional      1—3 5
Filtration      7
Filtration, augmentation      8 37
Filtration, Brownian      8
Filtration, canonical      7
Filtration, stopped      10
Fisk-Stratonovich integral      (see Integral)
Function, convex      5
Fundamental solution      (see Solution)
Hierarchical set      71
Increasing process      12
Increment, independent      8
Increment, stationary      8
Indicator function      1
Inequality, Doob’s      11 23
Inequality, Gronwall      38
Inequality, Jensen’s      5
Initial condition      37 43
Integral, Fisk — Stratonovich      36
Integral, Ito      20 21
Integral, Lebesgue — Stieltjes      12
Integral, multiple ltd      70
Integral, Stochastic      12 15 20 21
Integration by parts      35
Isometry      19
Ito formula, multi-dimensional      34
Ito formula, one-dimensional      27
Ito integral      (see Integral)
Ito isometry      19 21
Ito process      26
Ito process, d-dimensional      26
Ito stochastic differential equation      (see Stochastic differential equation)
Ito-Taylor approximation      (see Approximation)
Ito-Taylor scheme strong      78
Jensen’s Inequality      (see Inequality)
Linear growth condition      38
Lipschitz condition, global      38
Lipschitz condition, localization      24
Lipschitz condition, sequence      11
Ltd coefficient function      (see Coefficient function)
Marsaglias Polar Method      (see Transformation)
Martingale      9
Martingale, continuous local      11
Martingale, exponential      35
Martingale, local      11 25
Mean-square approximation      (see Approximation)
Measurable process      (see Stochastic process)
Measurable space      12
Measure, Lebesgue      5
Milstein scheme      78
Moment generating function      54
Monte Carlo, simulation      48
Multi-index      70
Multiple Ito integral      (see Integral)
Multiplicative noise      (see Noise)
Noise, additive      45 47 69 79
Noise, commutative      80
Noise, diagonal      79
Noise, multiplicative      45
Norm, $L^{2}$-norm      18
Norm, $L_{T}$-norm      19
Norm, T-norm      19
One-step approximation seeapproximation      61
Optional sampling theorem      10
Optional time      10
Ornstein — Uhlenbeck process      35
Polynomial growth      59
Probability, conditional      1 2
Progressively measurable      (see Stochastic process)
pseudorandom number      (see Random number)
Pseudorandom number generator      (see Random number generator)
Quadratic cross-variation process      (see Variation)
Quadratic variation process      (see Variation)
Random number      48
Random number generator      48
Random number generator, Fibonacci generator      50
Random number generator, full period      49
Random number generator, inversive congruential generator      50
Random number generator, lagged Fibonacci generator      50
Random number generator, linear congruence generator      48
Random number generator, multiplicative congruence generator      48
Random number, pseudo      48
Random variable, discrete      1
Remainder set      71
Sample path      7
Sampling method, inverse transform method      51
Seed      48
Solution, existence      38
Solution, fundamental      43
Solution, strong      37
Solution, uniqueness      38
Step size      57
Stochastic differential equation      37
Stochastic differential equation, homogeneous      43
Stochastic differential equation, inhomogeneous      43
Stochastic differential equation, Ito      46
Stochastic differential equation, linear      43
Stochastic differential equation, Stratonovich      46
Stochastic integral      (see Integral)
Stochastic process      7
Stochastic process, adapted      7
Stochastic process, continuous time      7
Stochastic process, discrete time      7
Stochastic process, equivalence      19
Stochastic process, finite-dimensional distribution      8
Stochastic process, indistinguishable      7
Stochastic process, measurable      17
Stochastic process, modification      7
Stochastic process, progressively measurable      17
Stochastic process, simple      15
Stochastic process, stopped      10
Stochastic Taylor expansion      (see Taylor expansion)
Stopping time      10
Stratonovich integral      (see Fisk-Stratonovich integral)
Stratonovich stochastic differential equation      (see Stochastic differential equation)
Strong approximation      (see Approximation)
Strong uniqueness      38
Sub-martingale      9
Super-martingale      9
Taylor approximation      (see Approximation)
Taylor expansion, Ito      71
Taylor expansion, stochastic      69 70
Trajectory      7
Transformation method      54
Transformation, Box — Muller method      55
Transformation, Marsaglias Polar Method      56
Usual conditions      9
Variation of a process      13
Variation of parameters method      43
Variation, quadratic cross-variation process      26
Variation, quadratic variation process      26
Vector space      18
Volatility      9
Weak approximation      (see Approximation)
Wiener process      8
Wiener process, quadratic variation      34
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