Probabilistic interpretation for system of conservation law arising in adhesion particle dynamics

This Note presents a construction of a solution for the nonlinear stochastic differential equation X-t = X-0 + integral(0)(t) E[mu(0)(X-0)\X-s]ds, t greater than or equal to 0. The random X-0 with values in R and the function mu(0) are given. We denote by P-t the probability distribution of X-t and mu(x,t) = E[mu(0)(X-0)\X-t = x]. We prove that (P-t, mu(.,t), t greater than or equal to 0) is a weak solution for system of conservation law arising in adhesion particle dynamics. (C) Academie des Sciences/Elsevier, Paris.