On a Continuous Analog of the Parabolic Anderson Model
Анотація
We consider a stochastic equation in ℝ d , whose nonlocal part is a convolution operator with nonnegative symbol and the local part is an operator of multiplication by an ergodic field in ℝ d . We present the upper and lower bounds for its solutions corresponding to the constant initial data and present an example of the field for which these bounds coalesce as t → ∞ resulting in an asymptotic formula for the logarithm of the solution. We also briefly discuss the spectral aspect of our results.
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