Abstract. We consider a system of interacting diffusions on the integer lattice. By letting the mesh size go to zero and by using a suitable scaling, we show that the system converges (in a strong sense) to a solution of the stochastic heat equation on the real line. As a consequence, we obtain comparison inequalities for product moments of the stochastic heat equation with different nonlinearities.
Keywords. Stochastic PDEs, comparison theorems, white noise.
AMS Classification (2000). Primary. 60H15; Secondary. 35K57.
Support. Research supported in part by the United States National Science Foundation grants DMS-0747758 (M.J.), DMS-1306470 (M.J. and D.K.), and DMS-1102646 (C.M.).
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Mathew Joseph Department of Probability and Statistics University of Sheffield Sheffield, England S3 7RH, UK m.joseph@sheffield.ac.uk |
Davar Khoshnevisan Department of Mathematics University of Utah 155 S, 1400 E JWB 233 Salt Lake City, UT 84112-0090, U.S.A. davar@math.utah.edu |
Carl Mueller Department of Mathematics University of Rochester Rochester, NY 14627, U.S.A. carl.2013@outlook.com |
Last Update: August 24, 2014
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2014 - Mathew Joseph, Davar Khoshnevisan, and Carl Mueller