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math.PR2022
On the valleys of the stochastic heat equation
Davar Khoshnevisan, Kunwoo Kim, Carl Mueller
We consider a generalization of the parabolic Anderson model driven by space-time white noise, also called the stochastic heat equation, on the real line. High peaks of solutions h…
math.PR2022
The compact support property for solutions to the stochastic partial differential equations with colored noise
Beom-Seok Han, Kunwoo Kim, Jaeyun Yi
We study the compact support property for solutions of the following stochastic partial differential equations: $$\partial_t u = a^{ij}u_{x^ix^j}(t,x)+b^{i}u_{x^i}(t,x)+cu+h(t,x,u(…