Strong invariance and noise-comparison principles for some parabolic stochastic PDEs

Mathew Joseph ^[1] ; Davar Khoshnevisan ^[1] ; Carl Mueller ^[2]
1. [1] University of Utah
  
  University of Utah
  
  Estados Unidos
2. [2] University of Rochester
  
  University of Rochester
  
  City of Rochester, Estados Unidos
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 1, 2017, págs. 377-403
Idioma: inglés
DOI: 10.1214/15-AOP1009
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Resumen
- 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.