论文信息 - Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process

Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process

The Euler scheme is a well-known method of approximation of solutions of stochastic differential equations (SDEs). A lot of results are now available concerning the precision of this approximation in case of equations driven by a drift and a Brownian motion. More recently, people got interested in the approximation of solutions of SDEs driven by a general Levy process. One of the problem when we use Levy processes is that we cannot simulate them in general and so we cannot apply the Euler scheme. We propose here a new method of approximation based on the cutoff of the small jumps of the Levy process involved. In order to find the speed of convergence of our approximation, we will use results about stability of the solutions of SDEs.

Sylvain Rubenthaler | Sylvain Rubenthaler

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