Numerical Integration Of Stochastic Differential Equations Book

	Introduction	1
Ch. 1	Mean-square approximation of solutions of systems of stochastic differential equations	11
1	Theorem on the order of convergence (theorem on the relation between approximation on a finite interval and one-step approximation)	11
2	Methods based on an analog of Taylor expansion of the solution	23
3	Explicit and implicit methods of order 3/2 for systems with additive noises	37
4	Optimal integration methods for linear systems with additive noises	56
5	A strengthening of the main convergence theorem	63
Ch. 2	Modeling of Ito integrals	75
6	Modeling Ito integrals depending on a single noise	75
7	Modeling Ito integrals depending on several noises	90
Ch. 3	Weak approximation of solutions of systems of stochastic differential equations	101
8	One-step approximation	101
9	The main theorem on convergence of weak approximations and methods of order of accuracy two	112
10	A method of order of accuracy three for systems with additive noises	118
11	An implicit method	127
12	Reducing the error of the Monte-Carlo method	130
Ch. 4	Application of the numerical integration of stochastic equations for the Monte-Carlo computation of Wiener integrals	135
13	Methods of order of accuracy two for computing Wiener integrals of functionals of integral type	135
14	Methods of order of accuracy four for computing Wiener integrals of functionals of exponential type	145
	Bibliography	165
	Index	169