Weak Error for Stable Driven Stochastic Differential Equations: Expansion of the Densities

被引：16

作者：

Konakov, Valentin ^{[2
]}

Menozzi, Stephane ^{[1
]}

机构：

[1] Univ Paris 07, LPMA, F-75013 Paris, France

[2] Acad Sci, CEMI, Moscow 117418, Russia

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2011年 / 24卷 / 02期

关键词：

Symmetric stable processes; Parametrix; Euler scheme; EULER SCHEME; LIMIT-THEOREMS; APPROXIMATION; DIFFUSIONS;

D O I：

10.1007/s10959-010-0291-x

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Consider a multidimensional stochastic differential equation of the form X(t) = x + integral(t)(0) b(X(s-))ds + integral(t)(0) f (X(s-))dZ(s), where (Z (s) ) (s >= 0) is a symmetric stable process. Under suitable assumptions on the coefficients, the unique strong solution of the above equation admits a density with respect to Lebesgue measure, and so does its Euler scheme. Using a parametrix approach, we derive an error expansion with respect to the time step for the difference of these densities.

引用

页码：454 / 478

页数：25

共 27 条

[1]

[Anonymous], STOCHASTIC ANAL APPL

[2]

[Anonymous], 1963, Markov Processes

[3] The law of the Euler scheme for stochastic differential equations .1. Convergence rate of the distribution function [J].