The Annals of Probability

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

Robert J. Adler and Gennady Samorodnitsky

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Abstract

We consider the full weak convergence, in appropriate function spaces, of systems of noninteracting particles undergoing critical branching and following a self-similar spatial motion with stationary increments. The limit processes are measure-valued, and are of the super and historical process type. In the case in which the underlying motion is that of a fractional Brownian motion, we obtain a characterization of the limit process as a kind of stochastic integral against the historical process of a Brownian motion defined on the full real line.

Article information

Source
Ann. Probab., Volume 23, Number 2 (1995), 743-766.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988287

Digital Object Identifier
doi:10.1214/aop/1176988287

Mathematical Reviews number (MathSciNet)
MR1334169

Zentralblatt MATH identifier
0841.60068

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60G17: Sample path properties 60G18: Self-similar processes 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
Self-similar processes fractional Brownian motion super process historical process

Citation

Adler, Robert J.; Samorodnitsky, Gennady. Super Fractional Brownian Motion, Fractional Super Brownian Motion and Related Self-Similar (Super) Processes. Ann. Probab. 23 (1995), no. 2, 743--766. doi:10.1214/aop/1176988287. https://projecteuclid.org/euclid.aop/1176988287


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