Articlebronze2008

Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process

51 citations0/0 files storedThe Annals of Applied Probability

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Markov Chains and Monte Carlo Methods

Abstract

We study some recursive procedures based on exact or approximate Euler schemes with decreasing step to compute the invariant measure of Lévy driven SDEs. We prove the convergence of these procedures toward the invariant measure under weak conditions on the moment of the Lévy process and on the mean-reverting of the dynamical system. We also show that an a.s. CLT for stable processes can be derived from our main results. Finally, we illustrate our results by several simulations.

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References

2005Stochastic Integration and Differential Equations 1990Stochastic Integration and Differential Equations 2001Lévy processes : theory and applications 2001Approximations of small jumps of Lévy processes with a view towards simulation 1997The Euler scheme for Lévy driven stochastic differential equations 2005Pricing electricity derivatives under alternative stochastic spot price models

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