论文信息 - Error Analysis for Approximation of Stochastic Differential Equations Driven by Poisson Random Measures

Error Analysis for Approximation of Stochastic Differential Equations Driven by Poisson Random Measures

Let Xt be the solution of a stochastic differential equation (SDE) with starting point x0 driven by a Poisson random measure. Additive functionals are of interest in various applications. Nevertheless they are often unknown and can only be found by simulation on computers. We investigate the quality of the Euler approximation. Our main emphasis is on SDEs driven by an $\alpha$-stable process, $0<\alpha < 2$, where we study the approximation of the Monte Carlo error ${\Bbb E} [f(X_T)]$, f belonging to ${L}^\infty$. Moreover, we treat the case where the time equals $T\wedge \tau$, where $\tau$ is the first exit time of some interval.

Erika Hausenblas | E. Hausenblas

[1] Michael Cranston,et al. The malliavin calculus for pure jump processes and applications to local time , 1986 .

[2] Philip Protter,et al. Wong-Zakai Corrections, Random Evolutions, and Simulation Schemes for SDE's , 1991 .

[3] Denis Talay,et al. The law of the Euler scheme for stochastic differential equations , 1996, Monte Carlo Methods Appl..

[4] P. Protter. Stochastic integration and differential equations , 1990 .

[5] R. Wolpert. Lévy Processes , 2000 .

[6] J. Jacod,et al. Malliavin calculus for processes with jumps , 1987 .

[7] D. Talay,et al. The law of the Euler scheme for stochastic differential equations , 1996 .

[8] Philip Protter,et al. The Euler scheme for Lévy driven stochastic differential equations , 1997 .

[9] Denis Talay,et al. Probabilistic numerical methods for partial differential equations: Elements of analysis , 1996 .

[10] Marc Yor,et al. Inequalities for a Pair of Processes Stopped at a Random Time , 1986 .

[11] Jean Jacod,et al. Semimartingales and Markov processes , 1980 .

[12] Erhan Çinlar,et al. Representation of Semimartingale Markov Processes in Terms of Wiener Processes and Poisson Random Measures , 1981 .

[13] I. Gihman,et al. Stochastic Differential Equations , 1975 .

[14] E. Gobet. Weak approximation of killed diffusion using Euler schemes , 2000 .

[15] S. Kanagawa,et al. The Rate of Convergence for Approximate Solutions of Stochastic Differential Equations , 1989 .