Hypoelliptic Random Heat Kernels: a Case Study
نویسنده
چکیده
We consider the fundamental solution of a simple hypoelliptic stochastic partial differential equation in which the first-order term is modulated by white noise. We derive some short-time asymptotic formulæ. We discover that the form of the dominant short-time asymptotics depends nontrivially upon the interplay between the geometry of the noisy first-order term and the geometry defined by the hypoelliptic operator.
منابع مشابه
Short-time Asymptotics of Heat Kernels for a Class of Hypoelliptic Operators
We compute the short-time asymptotics of heat kernels for a family of hypoelliptic operators, and we relate these to the value function of an associated variational problem previously investigated in the control theory literature. These heat kernels generalize to the noncontact case a heat kernel that has been previously obtained for the contact hypoelliptic Laplacian defined on the Heisenberg ...
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