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We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Levy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the Levy process with a high order scheme for the Brownian driven component, applied between the jump times. The overall approximation is analyzed using a stochastic splitting argument. The resulting error bound involves separate contributions of the compound Poisson approximation and of the discretization scheme for the Brownian part, and allows, on one hand, to balance the two contributions in order to minimize the computational time, and on the other hand, to study the optimal design of the approximating compound Poisson process. For driving processes whose Levy measure explodes near zero in a regularly varying way, this procedure allows to construct discretization schemes with arbitrary order of convergence.
We construct an efficient integrator for stochastic differential systems driven by Levy processes. An efficient integrator is a strong approximation that is more accurate than the corresponding stochastic Taylor approximation, to all orders and indep
In this paper, we study almost periodic solutions for semilinear stochastic differential equations driven by L{e}vy noise with exponential dichotomy property. Under suitable conditions on the coefficients, we obtain the existence and uniqueness of bo
We develop algorithms for computing expectations of the laws of models associated to stochastic differential equations (SDEs) driven by pure Levy processes. We consider filtering such processes and well as pricing of path dependent options. We propos
We propose an unbiased Monte-Carlo estimator for $mathbb{E}[g(X_{t_1}, cdots, X_{t_n})]$, where $X$ is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a well-chosen sim
This paper deals with linear stochastic partial differential equations with variable coefficients driven by L{e}vy white noise. We first derive an existence theorem for integral transforms of L{e}vy white noise and prove the existence of generalized