A stochastic perturbation method for studying inverse problems of dynamics

Abstract

In this paper we introduce a method for the local reconstruciton of an analytical vector field ƒ in ℝⁿ from a set of observations about the asymptotics of n different brownian motions driven by ƒ. The case n = 2 is studied in details and an inversion algorithm is proposed. Although such algorithm turns out to be unstable, it can be a starting point for the quantitative analysis of some inverse problems in dissipative dynamics.

Keywords:

• Inverse problems in dynamics
• Diffusion stochastic processes
• Linear PDEs