Weak convergence of Markovian random evolution in a multidimensional space

2011/12/29 by Igor Samoilenko, Samoilenko, Igor V.
Economics, Econometrics and Finance · Mathematics · #60B10 Secondary: 60K35 #60F17 #60J60 #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary: 60K99 #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1112.6242

openalex publication_date 2011/12/29 · openalex created_date 2018/03/29 · openalex updated_date 2026/07/28

Abstract

We study Markovian symmetry and non-symmetry random evolutions in Rⁿ. Weak convergence of Markovian symmetry random evolution to Wiener process and of Markovian non-symmetry random evolution to a diffusion process with drift is proved using problems of singular perturbation for the generators of evolutions. Relative compactness in D_Rⁿ×Θ[0,∞) of the families of Markovian random evolutions is also shown.

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