Probabilistic Interpretation of Sticky Particle Model
Probabilistic Interpretation of Sticky Particle Model
复制标题
粘性粒子模型的概率解释
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
A. Dermoune
中科院分区：
文献类型：
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作者：
A. Dermoune
本文构造了非线性随机微分方程$X_t= X_0+ int_0^t mathbb{E}[u_0(X_0)|X_s]ds, t geq 0$的一个解。给出了值为$mathb{R}$的随机变量$X_0$和函数$u_0$。我们用$P_t$表示$X_t$和$u(x,t) = mathbb{E}[u_0(X_0)|X_t= x]$的概率分布。我们证明了$(P_t,u(cdot,t), tgeq 0)$是粘着粒子动力学中守恒律系统的弱解。
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 $(P_t,u(cdot,t), tgeq 0)$ is a weak solution for a system of conservation laws arising in adhesion particle dynamics.