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Firstly, we shall introduce the so-called snapping out Walshs Brownian motion and present its relation with Walshs Brownian motion. Then the stiff problem related to Walshs Brownian motion will be described and we shall build a phase transition for it. The snapping out Walshs Brownian motion corresponds to the so-called semi-permeable pattern of this stiff problem.
In this paper, we will first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk. In order to verify the rationality of this simulation, w
In this paper, we study the well-posedness of multi-dimensional backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with diagonal generators, the $z$ parts of whose $l$-th components only depend on the $l$-th columns.
In this paper we will study a stiff problem in two-dimensional space and especially its probabilistic counterpart. Roughly speaking, the heat equation with a parameter $varepsilon>0$ is under consideration: [ partial_t u^varepsilon(t,x)=frac{1}{2} ab
This is a summary (in French) of my work about brownian motion and Kac-Moody algebras during the last seven years, presented towards the Habilitation degree.
To extend several known centered Gaussian processes, we introduce a new centered mixed self-similar Gaussian process called the mixed generalized fractional Brownian motion, which could serve as a good model for a larger class of natural phenomena. T