Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow

Albeverio S, Hilbert A, Kolokoltsov V (2012)
Stochastics An International Journal of Probability and Stochastic Processes 84(2-3): 315-333.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We analyse the asymptotic behaviour of the heat kernel defined by a stochastically perturbed geodesic flow on the cotangent bundle of a Riemannian manifold for small time and small diffusion parameter. This extends Wentzel-Kramers-Brillouin-type methods to a particular case of a degenerate Hamiltonian. We give uniform bounds for the solution of the degenerate Hamiltonian boundary value problem for small time. The results are exploited to derive two-sided estimates and multiplicative asymptotics for the heat kernel semigroup and its trace.
Erscheinungsjahr
Zeitschriftentitel
Stochastics An International Journal of Probability and Stochastic Processes
Band
84
Zeitschriftennummer
2-3
Seite
315-333
ISSN
eISSN
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Albeverio S, Hilbert A, Kolokoltsov V. Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow. Stochastics An International Journal of Probability and Stochastic Processes. 2012;84(2-3):315-333.
Albeverio, S., Hilbert, A., & Kolokoltsov, V. (2012). Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow. Stochastics An International Journal of Probability and Stochastic Processes, 84(2-3), 315-333. doi:10.1080/17442508.2010.519029
Albeverio, S., Hilbert, A., and Kolokoltsov, V. (2012). Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow. Stochastics An International Journal of Probability and Stochastic Processes 84, 315-333.
Albeverio, S., Hilbert, A., & Kolokoltsov, V., 2012. Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow. Stochastics An International Journal of Probability and Stochastic Processes, 84(2-3), p 315-333.
S. Albeverio, A. Hilbert, and V. Kolokoltsov, “Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow”, Stochastics An International Journal of Probability and Stochastic Processes, vol. 84, 2012, pp. 315-333.
Albeverio, S., Hilbert, A., Kolokoltsov, V.: Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow. Stochastics An International Journal of Probability and Stochastic Processes. 84, 315-333 (2012).
Albeverio, Sergio, Hilbert, Astrid, and Kolokoltsov, Vassily. “Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow”. Stochastics An International Journal of Probability and Stochastic Processes 84.2-3 (2012): 315-333.