We give a new proof of the fact that the solutions of the stochastic heat equation, started with nonnegative initial conditions, are strictly positive at positive times. The proof uses concentration ...
The Annals of Probability, Vol. 43, No. 6 (November 2015), pp. 3006-3051 (46 pages) We study the nonlinear stochastic heat equation in the spatial domain ℝ, driven by space-time white noise. A central ...
The study of controllability for parabolic and heat equations focuses on the capability to steer the temporal evolution of diffusion-dominated processes towards desired states. Central to this field ...
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