Joint density for the local times of continuous-time Markov chains: Extended version

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dc.creatorBrydges, D.
dc.creatorvan der Hofstad, R.
dc.creatorKonig, W.
dc.date2005-11-07
dc.date2006-09-04
dc.date.accessioned2026-07-07T06:50:54Z
dc.date.available2026-07-07T06:50:54Z
dc.descriptionWe investigate the local times of a continuous-time Markov chain on an arbitrary discrete state space. For fixed finite range of the Markov chain, we derive an explicit formula for the joint density of all local times on the range, at any fixed time. We use standard tools from the theory of stochastic processes and finite-dimensional complex calculus. We apply this formula in the following directions: (1) we derive large deviation upper estimates for the normalized local times beyond the exponential scale, (2) we derive the upper bound in Varadhan's \chwk{l}emma for any measurable functional of the local times, \ch{and} (3) we derive large deviation upper bounds for continuous-time simple random walk on large subboxes of $\Z^d$ tending to $\Z^d$ as time diverges. We finally discuss the relation of our density formula to the Ray-Knight theorem for continuous-time simple random walk on $\Z$, which is analogous to the well-known Ray-Knight description of Brownian local times. In this extended version, we prove that the Ray-Knight theorem follows from our density formula.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math/0511169
dc.identifierhttp://arxiv.org/abs/math/0511169
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/104813
dc.subjectProbability
dc.subject60J27; 60J55; 15A75
dc.titleJoint density for the local times of continuous-time Markov chains: Extended version
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