By Ciprian A. Tudor
Self-similar strategies are stochastic methods which are invariant in distribution lower than appropriate time scaling, and are an issue intensively studied within the previous couple of many years. This booklet provides the elemental houses of those strategies and specializes in the examine in their version utilizing stochastic research. whereas self-similar tactics, and particularly fractional Brownian movement, were mentioned in numerous books, a few new periods have lately emerged within the medical literature. Some of them are extensions of fractional Brownian movement (bifractional Brownian movement, subtractional Brownian movement, Hermite processes), whereas others are recommendations to the partial differential equations pushed through fractional noises.
In this monograph the writer discusses the fundamental homes of those new periods of self-similar strategies and their interrelationship. even as a brand new procedure (based on stochastic calculus, particularly Malliavin calculus) to learning the habit of the differences of self-similar approaches has been built during the last decade. This paintings surveys those contemporary thoughts and findings on restrict theorems and Malliavin calculus.
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