By Ciprian A. Tudor

Self-similar approaches are stochastic tactics which are invariant in distribution below appropriate time scaling, and are an issue intensively studied within the previous few many years. This booklet offers the fundamental houses of those procedures and makes a speciality of the learn in their edition utilizing stochastic research. whereas self-similar procedures, and particularly fractional Brownian movement, were mentioned in different books, a few new periods have lately emerged within the clinical literature.  Some of them are extensions of fractional Brownian movement (bifractional Brownian movement, subtractional Brownian movement, Hermite processes), whereas others are ideas to the partial differential equations pushed by way of 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, specially Malliavin calculus) to learning the habit of the diversities of self-similar methods has been built during the last decade. This paintings surveys those fresh concepts 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

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