Super Fractional Brownian Motion, Fractional Super Brownian Motion and Related Self-Similar (Super) Processes

Self-Similar Processes, Fractional Brownian Motion and Statistical Inference

Self-similar stochastic processes are used for stochastic modeling whenever it is expected that long range dependence may be present in the phenomenon under consideration. After discusing some basic concepts of self-similar processes and fractional Brownian motion, we review some recent work on parametric and nonparametric inference for estimation of parameters for linear systems of stochastic ...

Occupation Time Large Deviations for Critical Branching Brownian Motion, Super-brownian Motion and Related Processes

We derive a large deviation principle for the occupation time functional, acting on functions with zero Lebesgue integral, for both superBrownian motion and critical branching Brownian motion in three dimensions. Our technique, based on a moment formula of Dynkin, allows us to compute the exact rate functions, which differ for the two processes. Obtaining the exact rate function for the super-B...

Avoiding-probabilities for Brownian Snakes and Super-brownian Motion Avoiding-probabilities for Brownian Snakes and Super-brownian Motion

We investigate the asymptotic behaviour of the probability that a normalized d-dimensional Brownian snake (for instance when the lifetime process is an excursion of height 1) avoids 0 when starting at distance " from the origin. In particular we show that when " tends to 0, this probability respectively behaves (up to multiplicative constants) like " 4 , " 2 p 2 and " (p 17?1)=2 , when d = 1, d...

Avoiding-probabilities for Brownian snakes and super-Brownian motion

We investigate the asymptotic behaviour of the probability that a normalized d-dimensional Brownian snake (for instance when the life-time process is an excursion of height 1) avoids 0 when starting at distance ε from the origin. In particular we show that when ε tends to 0, this probability respectively behaves (up to multiplicative constants) like ε, ε √ 2 and ε √ 17−1)/2, when d = 1, d = 2 a...

The average density of super-Brownian motion