Abstract
We study discrete nonlinear parabolic stochastic heat equations of the form, un+1(x)-un(x) = (Lun)(x)+ σ(u n(x))ζn(x), for n ∈ Z+ and x ∈ Zd, where ζ := {ζn(x)} n≥0,x∈Zd denotes random forcing and L the generator of a random walk on Zd. Under mild conditions, we prove that the preceding stochastic PDE has a unique solution that grows at most exponentially in time. And that, under natural conditions, it is "weakly intermittent." Along the way, we establish a comparison principle as well as a finite support property.
Original language | English |
---|---|
Pages (from-to) | 1042-1060 |
Number of pages | 19 |
Journal | Bernoulli |
Volume | 18 |
Issue number | 3 |
Early online date | 28 Jun 2012 |
DOIs | |
Publication status | Published - 31 Aug 2012 |
Externally published | Yes |
Keywords
- intermittency
- stochastic heat equations