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| Rößler A. — Numerical Methods for Stochastic Differential Equations |
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| Предметный указатель |
![$H^{2}[0, T]$](/math_tex/8b49954d84c779639c98fb58fd58981b82.gif) 24
![$L^{2}[0, T]$](/math_tex/41983e5353863709f987bad230d0467582.gif) 18
 20
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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,  -norm 18
Norm,  -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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