Semi-discrete semi-linear parabolic spdes

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題名:	Semi-discrete semi-linear parabolic spdes
作者:	須上苑;Georgiou, Nicos;Joseph, Mathew;Khoshnevisan, Davar;Shiu, Shang-Yuan
貢獻者:	理學院數學系
關鍵詞:	47B80;60H25;60J60;60K35;60K37;BDG inequality;comparison principle;discrete space;dissipative behavior;interacting diffusions;Lyapunov exponents;Mathematical problems;Noise;Parabolas;parabolic Anderson model;semi-discrete stochastic heat equation;The stochastic heat equation
日期:	2015-01-01
上傳時間:	2026-04-23 16:22:13 (UTC+8)
出版者:	Institute of Mathematical Statistics;Hayward: Institute of Mathematical Statistics
摘要:	摘要： Consider an infinite system $\partial_tu_t(x)=(\mathscr{L}u_t)(x)+ \sigma\bigl(u_t(x)\bigr)\partial_tB_t(x)$ of interacting Itô diffusions, started at a nonnegative deterministic bounded initial profile. We study local and global features of the solution under standard regularity assumptions on the nonlinearity σ. We will show that, locally in time, the solution behaves as a collection of independent diffusions. We prove also that the kth moment Lyapunov exponent is frequently of sharp order k2, in contrast to the continuous-space stochastic heat equation whose kth moment Lyapunov exponent can be of sharp order k3. When the underlying walk is transient and the noise level is sufficiently low, we prove also that the solution is a.s. uniformly dissipative provided that the initial profile is in ℓ1(Zd). 出版者： Hayward: Institute of Mathematical Statistics 出版日期： 2015-10-01 出處： The Annals of applied probability, 2015-10, Vol.25 (5), p.2959-3006 資源來源： JSTOR Arts and Sciences I 版權： Copyright © 2015 Institute of Mathematical Statistics 版權： Copyright Institute of Mathematical Statistics Oct 2015 版權： Copyright 2015 Institute of Mathematical Statistics 識別號： ISSN: 1050-5164 識別號： EISSN: 2168-8737 識別號： DOI: 10.1214/14-AAP1065
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