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Fluctuation and Rate of Convergence for the Stochastic Heat Equation in Weak Disorder. (arXiv:1807.03902v1 [math.PR])
来源于:arXiv
We consider the stochastic heat equation on $\mathbb R^d$ with multiplicative
space-time white noise noise smoothed in space. For $d\geq 3$ and small noise
intensity, the solution is known to converge to a strictly positive random
variable as the smoothing parameter vanishes. In this regime, we study the rate
of convergence and show that the pointwise fluctuations of the smoothened
solutions as well as that of the underlying martingale of the Brownian directed
polymer converge to a Gaussian limit. 查看全文>>