engleski

Markov Jump Processes Approximating a Non-Symmetric Generalized Diffusion

Consider a non-symmetric generalized diffusion X(⋅) in ℝ d determined by the differential operator $A(\mbox{; ; ; \boldmath{; ; ; $Missing close brace. In this paper the diffusion process is approximated by Markov jump processes X n (⋅), in homogeneous and isotropic grids G n ⊂ℝ d , which converge in distribution in the Skorokhod space D([0, ∞), ℝ d ) to the diffusion X(⋅). The generators of X n (⋅) 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 $\{; ; ; a_{; ; ; ij}; ; ; (\mbox{; ; ; \boldmath{; ; ; $Missing close brace fulfills an additional condition. The proposed construction offers a simple method for simulation of sample paths of non-symmetric generalized diffusion. Simulations are carried out in terms of jump processes X n (⋅). For piecewise constant functions a ij on ℝ d and piecewise continuous functions a ij on ℝ2 the construction and principal algorithm are described enabling an easy implementation into a computer code.

Symmetric diffusion; Approximation of diffusion; Simulation of diffusion; Divergence form operators

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