96 citations · 152 across the 20 of their papers we have counts for
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Application of Stochastic Flows to the Sticky Brownian Motion Equation
Hatem Hajri, Caglar Mine, Marc Arnaudon
We show how the theory of stochastic flows allows to recover in an elementary way a well known result of Warren on the sticky Brownian motion equation.
On a coupling of solutions to the interface SDE on a star graph
Hatem Hajri, Marc Arnaudon
Inspired by Tsirelson proof of the non Brownian character of WalshBrownian motion ltration on three or more rays, we prove some results on aparticular coupling of solutions to the…
On flows associated to Tanaka's SDE and related works
Hatem Hajri
We review the construction of flows associated to Tanaka's SDE from [9] and give an easy proof of the classification of these flows by means of probability measures on [0, 1]. Our…
Stochastic flows and an interface SDE on metric graphs
Hatem Hajri, Olivier Raimond
This paper consists in the study of a stochastic differential equation on a metric graph, called an interface SDE . To each edge of the graph is associated an indepe…
Stochastic flows on metric graphs
Hatem Hajri, Olivier Raimond
We study a simple stochastic differential equation driven by one Brownian motion on a general oriented metric graph whose solutions are stochastic flows of kernels. Under some cond…
On the Csáki-Vincze transformation
Hatem Hajri
Cs aki and Vincze have de fined in 1961 a discrete transformation T which applies to simple random walks and is measure preserving. In this paper, we are interested in ergodic and…
Tanaka's equation on the circle and stochastic flows
Hatem Hajri, Olivier Raimond
We define a Tanaka's equation on an oriented graph with two edges and two vertices. This graph will be embedded in the unit circle. Extending this equation to flows of kernels, we…
Discrete approximation to solution flows of Tanaka SDE related to Walsh Brownian motion
Hatem Hajri
In a previous work, we have defined a Tanaka SDE related to Walsh Brownian motion which depends on kernels. It was shown that there are only one Wiener solution and only one flow o…
Stochastic flows related to Walsh Brownian motion
Hatem Hajri
We define an equation on a simple graph which is an extension of Tanaka equation and the skew Brownian motion equation. We then apply the theory of transition kernels developped by…