Dynkin’s Isomorphism Theorem and the Stochastic Heat Equation

Another Look into the Wong–zakai Theorem for Stochastic Heat Equation

Consider the heat equation driven by a smooth, Gaussian random potential: ∂tuε = 1 2 ∆uε + uε(ξε − cε), t > 0, x ∈ R, where ξε converges to a spacetime white noise, and cε is a diverging constant chosen properly. For any n > 1, we prove that uε converges in Ln to the solution of the stochastic heat equation. Our proof is probabilistic, hence provides another perspective of the general result of...

The First-Order Isomorphism Theorem

For any class C und closed under NC reductions, it is shown that all sets complete for C under first-order (equivalently, Dlogtimeuniform AC) reductions are isomorphic under first-order computable

The Norm Residue Isomorphism Theorem

We provide a patch to complete the proof of the Voevodsky-Rost Theorem, that the norm residue map is an isomorphism. (This settles the motivic Bloch-Kato conjecture).

Stochastic heat equation with white-noise drift

An Approximation Theorem of Runge Type for the Heat Equation

If ft is an open subset of Rn+ , the approximation problem is to decide whether every solution of the heat equation on II can be approximated by solutions defined on all of R . The necessary and sufficient condition on il which insures this type of approximation is that every section of Q taken by hyperplanes orthogonal to the Z-axis be an open set without "holes," i.e., whose complement has no...