On a continuous analog of the parabolic Anderson model - Kondratiev, Yu.; Pastur, L. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 519.21; 517.9 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.