Burgers equation with a stochastic initial value with homogeneous and independent increments

We study here solutions of inviscid Burgers equation with a stochastic initial value with homogeneous and independent increments without positive jumps. 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 equation if and only if the exponent functions psi (t, w) satisfy the differential equation: partial derivative(t)psi = i psi partial derivative(w) psi. The existence of such solutions follows then from the examination of that last equation. The case of a brownian initial condition is made explicit. (C) Elsevier, Paris.