An asymptotic theory for randomly forced discrete nonlinear heat equations

作者：Foondun Mohammud^*; Khoshnevisan Davar

来源：Bernoulli, 2012, 18(3): 1042-1060.

DOI：10.3150/11-BEJ357

• intermittency
• stochastic heat equations

We study discrete nonlinear parabolic stochastic heat equations of the form, u (n+1)(x) - u(n)(x) = (Lu-n)(x) + sigma(un(x)(x))xi(n) (x), for n epsilon Z(+) and x epsilon Z(d), where xi ;=(xi(n)(x)](n >= 0,) (d)(x is an element of Z) denotes random forcing and E the generator of a random walk on Z(d). 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.

• 出版日期2012-8