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MARKOV JUMP PROCESSES APPROXIMATING A NON-SYMMETRIC GENERALIZED DIFFUSION

By Nedzad Limic

Abstract

Consider a non-symetric generalized diffusion X(·) in R d determined by the differential operator A(x) = − ∑ ∑ ∂iaij(x)∂j + bi(x)∂i. In this paper the diffusion process ij i is approximated by Markov jump processes Xn(·) in homogeneous and isotropic grids Gn ⊂ R d which converge in distribution to diffusion. The generators of Xn(·) are constructed explicitly. Due to the homogeneity and isotropy of grids the proposed method for d ≥ 3 can be applied to processes for which the diffusion tensor {aij(x)} dd 11 fulfills an additional condition. The proposed construction offers a simple method for simulation of sample paths of non-symetric generalized diffusion. Simulations are carried out in terms of jump processes Xn(·). For d = 2 the construction can be easily implemented into a computer code

Topics: Key words, Symmetric diffusion, Approximation of diffusion, Simulation of diffusion, Divergence form
Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.313.1709
Provided by: CiteSeerX
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