By Ciprian A. Tudor
Self-similar strategies are stochastic procedures which are invariant in distribution less than compatible time scaling, and are an issue intensively studied within the previous few a long time. This publication provides the fundamental houses of those techniques and makes a speciality of the learn in their version 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 clinical literature. Some of them are extensions of fractional Brownian movement (bifractional Brownian movement, subtractional Brownian movement, Hermite processes), whereas others are strategies to the partial differential equations pushed by way of fractional noises.
In this monograph the writer discusses the elemental houses of those new periods of self-similar strategies and their interrelationship. whilst a brand new process (based on stochastic calculus, particularly Malliavin calculus) to learning the habit of the differences of self-similar strategies has been built over the past decade. This paintings surveys those fresh recommendations 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