Weak Error for Continuous Time Markov Chains Related to Fractional in Time P(I)DEs

2015/05/18 by M. Kelbert, Kelbert, M., V. Konakov +3 · 1 citation
Mathematics · #35R11 #60H30 #FOS: Mathematics #Primary 60F99 #Probability (math.PR) #Secondary 60G52 #math.PR #msc:35R11 #msc:60F99 #msc:60G52 #msc:60H30

paper · pdf · doi:10.48550/arxiv.1505.04610

36 pages

arxiv created 2015/05/18 · arxiv updated 2015/05/19

Abstract

We provide sharp error bounds for the difference between the transition densities of some multidimensional Continuous Time Markov Chains (CTMC) and the fundamental solutions of some fractional in time Partial (Integro) Differential Equations (P(I)DEs). Namely, we consider equations involving a time fractional derivative of Caputo type and a spatial operator corresponding to the generator of a non degenerate Brownian or stable driven Stochastic Differential Equation (SDE).

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• On the existence of stationary solutions for certain systems of integro-differential equations with the double scale anomalous diffusion

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