caa a22 4500 445842059 CHVBK 20180317145347.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00245-011-9133-1 doi (NATIONALLICENCE)springer-10.1007/s00245-011-9133-1 Limić Nedžad Dept. of Mathematics, University of Zagreb, Bijenička 30, 10002, Zagreb, Croatia aut Markov Jump Processes Approximating a Non-Symmetric Generalized Diffusion [Elektronische Daten] [Nedžad Limić] Consider a non-symmetric generalized diffusion X(⋅) in ℝ d determined by the differential operator $A(\mbox{\boldmath{$x$}})=-\sum_{ij}\partial_{i}a_{ij}(\mbox{\boldmath{$x$}})\partial_{j} +\sum_{i} b_{i}(\mbox{\boldmath{$x$}})\partial_{i}$ . 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 $\{a_{ij}(\mbox{\boldmath{$x$}})\}_{11}^{dd}$ 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 piece-wise constant functions a ij on ℝ d and piece-wise continuous functions a ij on ℝ2 the construction and principal algorithm are described enabling an easy implementation into a computer code. Springer Science+Business Media, LLC, 2011 Symmetric diffusion nationallicence Approximation of diffusion nationallicence Simulation of diffusion nationallicence Divergence form operators nationallicence Applied Mathematics & Optimization Springer-Verlag 64/1(2011-08-01), 101-133 0095-4616 64:1<101 2011 64 245 https://doi.org/10.1007/s00245-011-9133-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-011-9133-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Limić Nedžad Dept. of Mathematics, University of Zagreb, Bijenička 30, 10002, Zagreb, Croatia aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 64/1(2011-08-01), 101-133 0095-4616 64:1<101 2011 64 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer