Upper and lower limits of doubly perturbed Brownian motion

Doubly Perturbed Neutral Stochastic Functional Equations Driven by Fractional Brownian Motion

In this paper, we study a class of doubly perturbed neutral stochastic functional equations driven by fractional Brownian motion. Under some non-Lipschitz conditions, we will prove the existence and uniqueness of the solution to these equations by providing a semimartingale approximation of a fractional stochastic integration. AMS Subject Classifications: 60H15, 60G15, 60H05 Chinese Library Cla...

Some calculations for perturbed brownian motion

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Perturbed and Non-perturbed Brownian Taboo Processes

– In this paper we study the Brownian taboo process, which is a version of Brownian motion conditioned to stay within a finite interval, and the α-perturbed Brownian taboo process, which is an analogous version of an α-perturbed Brownian motion.We are particularly interested in the asymptotic behaviour of the supremum of the taboo process, and our main results give integral tests for upper and ...

Scaling Limits and Super-Brownian Motion, Volume 49, Number 9

Infinite canonical super-Brownian motion and scaling limits

We construct a measure valued Markov process which we call infinite canonical superBrownian motion, and which corresponds to the canonical measure of super-Brownian motion conditioned on non-extinction. Infinite canonical super-Brownian motion is a natural candidate for the scaling limit of various random branching objects on Zd when these objects are (a) critical; (b) mean-field and (c) infini...