The Rates of Convergence for Functional Limit Theorems withStable Subordinators and for CTRW Approximations toFractional Evolutionsстатья
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Аннотация:From the initial development of probability theory to the present days, the convergenceof various discrete processes to simpler continuous distributions remains at the heart of stochasticanalysis. Many efforts have been devoted to functional central limit theorems (also referred toas the invariance principle), dealing with the convergence of random walks to Brownian motion.Though quite a lot of work has been conducted on the rates of convergence of the weighted sums ofindependent and identically distributed random variables to stable laws, the present paper is thefirst to supply the rates of convergence in the functional limit theorem for stable subordinators. On the other hand, there is a lot of activity on the convergence of CTRWs (continuous time randomwalks) to processes with memory (subordinated Markov process) described by fractional PDEs. Oursecond main result is the first one yielding rates of convergence in such a setting. Since CTRWapproximations may be used for numeric solutions of fractional equations, we obtain, as a directconsequence of our results, the estimates for error terms in such numeric schemes.