Optimal lower bounds on hitting probabilities for non-linear systems of stochastic fractional heat equations

We consider a system of d non-linear stochastic fractional heat equations in spatial dimension 1 driven by multiplicative d-dimensional space–time white noise. establish sharp Gaussian-type upper bound on the two-point probability density function (u(s,y),u(t,x)). From this result, we deduce optimal lower bounds hitting probabilities process {u(t,x):(t,x)?[0,?[×R} non-Gaussian case, terms Newtonian capacity, which is as that Gaussian case. This also improves result Dalang et al. (2009) for systems classical equations. solution Hausdorff measure.