By Ciprian A. Tudor
Self-similar strategies are stochastic approaches which are invariant in distribution less than compatible time scaling, and are a subject matter intensively studied within the previous few a long time. This ebook provides the fundamental houses of those techniques and specializes in the examine in their edition utilizing stochastic research. whereas self-similar tactics, and particularly fractional Brownian movement, were mentioned in different 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 by way of fractional noises.
In this monograph the writer discusses the fundamental homes of those new sessions of self-similar strategies and their interrelationship. while a brand new method (based on stochastic calculus, particularly Malliavin calculus) to learning the habit of the differences of self-similar tactics has been built over the past decade. This paintings surveys those contemporary ideas and findings on restrict theorems and Malliavin calculus.
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Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach (Probability and Its Applications) by Ciprian A. Tudor