INTRINSIC STATISTICAL SOLUTIONS OF BURGERS-EQUATION AND LEVY PROCESSES

We study here solutions of inviscid Burgers equation with a stochastic initial value. We define the notion of intrinsic statistical solution of this evolution equation and show that a family (X (t); t greater than or equal to 0) of homogeneous Levy processes is an intrinsic statistical solution of Burgers Burgers equation if and only if the exponent functions psi (t, w) satisfy: partial derivative psi/partial derivative t = i psi, (partial derivative psi/partial derivative w).