Long time existence for the heat equation with a spatially correlated noise term
N. Franzova · Stochastic Analysis and Applications · 1999
We consider the equation ,with Dirichlet boundary conditions. [Ndot](t, x) denotes a twoparameter colored noise, which is a Gaussian process, but contrary to the often used white noise it is correlated in the space variable. Large deviation result estimates the probability of the noise term to become large during a given time interval. This then leads to the proof that for (here α indicates the size of the correlation) the solution exists for all time with probability 1. This extends the result known for the white noise