Theory of Probability and Mathematical Statistics
Weak convergence of a time and space scaled semi-Markov process to a limiting diffusion process
Vitaliy Golomoziy, Igor Malyk and Igor Samoilenko
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Abstract: We consider a semi-Markov process with values in ℝd and create a scheme of series with the help of time and space scaling. We prove the weak convergence in a Skorokhod space of such scaled processes to a limiting diffusion process under conditions on the distribution of jumps and holding times of the original semi-Markov process.
Keywords: Semi-Markov process, diffusion process, weak convergence, compensating operator
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