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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 and mild solutions of second order elliptic partial differential equations. Furthermore, we discuss the generalized electric Schrodinger operator for different potential functions $V$.
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 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
We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type. Whereas for ODEs the decomposition is intrinsic, for PDEs it is
Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and convolution qua
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 w