Backwards semi-martingales into Burgers' turtulence

Abstract

In fluid dynamics governed by the one dimensional inviscid Burgers equation ${\partial }_{t}u+u{\partial }_x(u)=0$, the stirring is explained by the sticky particles model. A Markov process $([Z_t^1,Z_t^2],t\ge 0)$ describes the motion of random turbulent intervals which evolve inside an other Markov process $([Z_t^3,Z_t^4],t\ge 0)$, describing the motion of random clusters concerned with the turbulence. Then, the four velocity processes $(u(Z_t^i,t),t\ge 0)$ are backward semi-martingales.

21 pages, 5 figures

References in corpus (1)

• An essay on the general theory of stochastic processes