A class of asymptotically self-similar stable processes with stationary increments

Discrete approximation of a stable self-similar stationary increments process

The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known about the context in which such processes can arise. To our knowledge, discretization and convergence theorems are available only in the case of stable Lévy motions and fra...

Maxima of Long Memory Stationary Symmetric Α-stable Processes, and Self-similar Processes with Stationary Max-increments

We derive a functional limit theorem for the partial maxima process based on a long memory stationary α-stable process. The length of memory in the stable process is parameterized by a certain ergodic theoretical parameter in an integral representation of the process. The limiting process is no longer a classical extremal Fréchet process. It is a self-similar process with α-Fréchet marginals, a...

Representations of Gaussian processes with stationary increments

Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments

We consider a family of stochastic processes built from infinite sums of independent positive random functions on R+. Each of these functions increases linearly between two consecutive negative jumps, with the jump points following a Poisson point process on R+. The motivation for studying these processes stems from the fact that they constitute simplified models for TCP traffic on the Internet...

Self-similar Processes with Independent Increments Associated with L Evy and Bessel Processes

1 Abstract Wolfe 1982 and Sato 1991 gave t wo diierent representations of a random variable X 1 with a self-decomposable distribution in terms of processes with independent increments. This paper shows how either of these representations follows easily from the other, and makes these representations more explicit when X 1 is either a rst or last passage time for a Bessel process.