ar X iv : 0 80 4 . 08 48 v 2 [ m at h . PR ] 2 2 M ar 2 00 9 MARKOV JUMP PROCESSES APPROXIMATING A NON - SYMMETRIC GENERALIZED DIFFUSION ∗
نویسنده
چکیده
Consider a non-symetric generalized diffusion X(·) in R d determined by the differential operator A(x) = − ij ∂iaij (x)∂j + i bi(x)∂i. In this paper the diffusion process 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.
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ar X iv : 0 80 4 . 08 48 v 1 [ m at h . PR ] 5 A pr 2 00 8 MARKOV JUMP PROCESSES APPROXIMATING A NONSYMMETRIC GENERALIZED DIFFUSION ∗
Consider a nonsymetric generalized diffusion X(·) in R d generated by the differential operator A(x) = ij ∂iaij(x)∂j + i bi(x)∂i. In this paper the diffusion process 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 grid...
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