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July 1999 Probabilistic Interpretation of Sticky Particle Model
Azzouz Dermoune
Ann. Probab. 27(3): 1357-1367 (July 1999). DOI: 10.1214/aop/1022677451

Abstract

This work presents a construction of a solution for the nonlinear stochastic differential equation $X_t= X_0+ \int_0^t \mathbb{E}[u_0(X_0)|X_s]ds, t \geq 0$. The random variable $X_0$ with values in $\mathb{R}$ and the function $u_0$ are given. We denote by $P_t$ the probability distribution of $X_t$ and $u(x,t) = \mathbb{E}[u_0(X_0)|X_t= x]$. We prove that $(P_t,u(\cdot,t), t\geq 0)$ is a weak solution for a system of conservation laws arising in adhesion particle dynamics.

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Azzouz Dermoune. "Probabilistic Interpretation of Sticky Particle Model." Ann. Probab. 27 (3) 1357 - 1367, July 1999. https://doi.org/10.1214/aop/1022677451

Information

Published: July 1999
First available in Project Euclid: 29 May 2002

zbMATH: 0960.60055
MathSciNet: MR1733152
Digital Object Identifier: 10.1214/aop/1022677451

Subjects:
Primary: 60H10, 60H15
Secondary: 60H30

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 3 • July 1999
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