کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1155403 | 958722 | 2016 | 16 صفحه PDF | دانلود رایگان |
In this work we are going to show weak convergence of probability measures. The measure corresponding to the solution of the following one dimensional nonlinear stochastic heat equation ∂∂tut(x)=κ2∂2∂x2ut(x)+σ(ut(x))ηα with colored noise ηαηα will converge to the measure corresponding to the solution of the same equation but with white noise ηη, as α↑1α↑1. Function σσ is taken to be Lipschitz and the Gaussian noise ηαηα is assumed to be colored in space and its covariance is given by E[ηα(t,x)ηα(s,y)]=δ(t−s)fα(x−y)E[ηα(t,x)ηα(s,y)]=δ(t−s)fα(x−y) where fαfα is the Riesz kernel fα(x)∝1/|x|αfα(x)∝1/|x|α. We will work with the classical notion of weak convergence of measures, that is convergence of probability measures on a space of continuous function with compact domain and sup–norm topology. We will also state a result about continuity of measures in αα, for α∈(0,1)α∈(0,1).
Journal: Stochastic Processes and their Applications - Volume 126, Issue 9, September 2016, Pages 2860–2875