Probabilistic interpretation of sticky particle model. (English) Zbl 0960.60055

Dermoune, Azzouz

Ann. Probab. 27, No. 3, 1357-1367 (1999).

It is given a probabilistic interpretation of the “sticky particle model”. Starting with a given random variable \(X_0\) on some probability space \((\Omega,{\mathcal F},\mu)\) it is proved that the equation \(X_t= X_0+ \int^t_0 E[u_0(X_0)\mid X_s]ds\) has a continuous solution \(X_t(\omega)\), \(t\geq 0\). As a consequence, defining \(u(x,t)= E[u_0(X_0)\mid X_t=x]\) and a measure \(dI_t=u (x,t)dP_t\), where \(P_t\) is the probability distribution of \(X_t\), then \((P_t, I_t,u (\cdot,t))_{t\geq 0}\) is a weak solution for a system of conservation laws. There are given and proved three theorems.

Reviewer: Constantin Vârsan (Bucureşti)

MSC:

60H10

Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

stochastic differential equations; weak solutions for a system of conservation laws

References:

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