Self-Similarity and Power Asymptotics for Families of Stochastic Processes
Who: Bent Jørgensen (University of Southern Denmark)
When: Friday, December 4, 2009 at 12:30
Where: The CP³ meeting room
Abstract: We extend the notion of self-similarity to one-parameter families of stochastic processes, including Hougaard Lévy processes such as for example Brownian motion with drift, the Poisson process, the inverse Gaussian process, and the gamma compound Poisson process. Such families are characterized by having exponential family structure and power variance functions, and have many properties in common with conventional self-similar processes. We introduce a class of fractional Hougaard motions by means of a stochastic integral representation similar to the moving average representation of fractional Brownian motion. We show that such self-similar families appear as limits in a Lamperti-type limit theorem for families of stochastic processes. These results characterize a considerable class of self-similar families of stochastic processes with finite variance, in contrast to conventional self-similarity, where only fractional Brownian motion has finite variance. This is joint work with J. R. Martínez and C.G.B. Demétrio.
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