Adaptive Weak Approximation of Diffusions with Jumps

E. Mordecki; A. Szepessy; R. Tempone; G. E. Zouraris

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Adaptive Weak Approximation of Diffusions with Jumps

E. Mordecki·A. Szepessy·R. Tempone·G. E. Zouraris

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Abstract

This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational error, with computable leading order term in a posteriori form, based on stochastic flows and discrete dual backward problems which extends the results in [STZ]. These expansions lead to efficient and accurate computation of error estimates. Adaptive algorithms for either stochastic time steps or quasi-deterministic time steps are described. Numerical examples show the performance of the proposed error approximation and of the described adaptive time-stepping methods.

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BibTeX RIS

E. Mordecki, A. Szepessy, R. Tempone, G. E. Zouraris. 2006-09-06. Adaptive Weak Approximation of Diffusions with Jumps. https://arxiv.org/abs/math/0609186

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