کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5127994 1489371 2018 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The non-locality of Markov chain approximations to two-dimensional diffusions
ترجمه فارسی عنوان
غیرمحلی بودن تقریب زنجیره مارکف برای انتشارهای دو بعدی
کلمات کلیدی
انتشار دو بعدی؛ تقسیم زنجیره مارکوف؛ طرح های تفاضل محدود یکنواخت
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
چکیده انگلیسی

In this short paper, we consider discrete-time Markov chains on lattices as approximations to continuous-time diffusion processes. The approximations can be interpreted as finite difference schemes for the generator of the process. We derive conditions on the diffusion coefficients which permit transition probabilities to match locally first and second moments. We derive a novel formula which expresses how the matching becomes more difficult for larger (absolute) correlations and strongly anisotropic processes, such that instantaneous moves to more distant neighbours on the lattice have to be allowed. Roughly speaking, for non-zero correlations, the distance covered in one timestep is proportional to the ratio of volatilities in the two directions. We discuss the implications to Markov decision processes and the convergence analysis of approximations to Hamilton-Jacobi-Bellman equations in the Barles-Souganidis framework.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Mathematics and Computers in Simulation - Volume 143, January 2018, Pages 176-185
نویسندگان
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