Excursion theory for Brownian motion indexed by the Brownian tree

Brownian Motion: The Link Between Probability and Mathematical Analysis

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Brownian Brownian Motion – I

A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work we study a 2D version of this model, where the molecule is a heavy disk of mass M ≫ 1 and the gas is represented by just one point particle of mass m = 1, which interacts with the disk and the walls of the container via elastic collisions. Chaotic behavior of...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Limiting Behaviors for Brownian Motion Reflected on Brownian Motion

Suppose that g(t) and Wt are independent Brownian motions starting from g(0) = W0 = 0. Consider the Brownian motion Yt reflected on g(t), obtained from Wt by the means of the Skorohod lemma. The upper and lower limiting behaviors of Yt are presented. The upper tail estimate on exit time is computed via principal eigenvalue.

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...