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math.PR2022★ 1 cited
The short memory limit for long time statistics in a stochastic Coleman-Gurtin model of heat conduction
Nathan E. Glatt-Holtz, Vincent R. Martinez, Hung D. Nguyen
We consider a class of semi-linear differential Volterra equations with polynomial-type potentials that incorporates the effects of memory while being subjected to random perturbat…
math.PR2021★ 5 cited
On the long-time statistical behavior of smooth solutions of the weakly damped, stochastically-driven KdV equation
Nathan Glatt-Holtz, Vincent R. Martinez, Geordie H. Richards
This paper considers the damped periodic Korteweg-de Vries (KdV) equation in the presence of a white-in-time and spatially smooth stochastic source term and studies the long-time b…