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Mathematics > Probability

arXiv:1410.0341 (math)
[Submitted on 1 Oct 2014]

Title:Strongly degenerate time inhomogeneous SDEs: densities and support properties. Application to a Hodgkin-Huxley system with periodic input

Authors:Reinhard Höpfner, E. Löcherbach, M. Thieullen
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Abstract:In this paper we study the existence of densities for strongly degenerate stochastic differential equations (SDEs) whose coefficients depend on time and are not globally Lipschitz. In these models neither local ellipticity nor the strong Hörmander condition is satisfied. In this general setting we show that continuous transition densities indeed exist in all neighborhoods of points where the weak Hörmander condition is satisfied. We also exhibit regions where these densities remain positive. We then apply these results to stochastic Hodgkin-Huxley models with periodic input as a first step towards the study of ergodicity properties of such systems in the sense of [27]-[28].
Comments: 35 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1310.7373
Subjects: Probability (math.PR)
Cite as: arXiv:1410.0341 [math.PR]
  (or arXiv:1410.0341v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1410.0341

Submission history

From: Michele Thieullen [view email]
[v1] Wed, 1 Oct 2014 19:29:15 UTC (1,366 KB)
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