Abstract
Stochastic partial differential equations constitute a relatively new subject. There have been a number of interesting papers in the last few years, but the field is still in its infancy if compared with the highly developed theory of stochastic ordinary differential equations. In this paper we report on a study of a non linear heat equation in a finite interval of space subject to a white noise forcing term. Due to the non linearity the equation, without the forcing term, exhibits several equilibrium configurations two of which are stable, actually asymptotically stable. The solution of the complete forced equation is a stochastic process in space and time with continuous sample paths whose behaviour we study in the limit of small noise. We obtain lower and upper bounds for the probability of large fluctuations and then apply our estimates to the calculation of the transition probability between the stable configurations (tunneling).
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