Hypoelliptic random heat kernels: A case study
نویسندگان
چکیده
منابع مشابه
Hypoelliptic Random Heat Kernels: a Case Study
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 h...
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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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We use the heat kernel on a compact oriented Riemannian manifold to assign to a sequence of cycles C1, . . . , Ck a real number (C1, . . . , Ck), provided the Ci satisfy certain conditions. If k = 2 then (C1, C2) will be the ordinary topological linking number, an integer, while if k ≥ 3 then (C1, . . . , Ck) will involve also iterated integrals of harmonic forms representing the Poincare duals...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05822-6