55,194 research outputs found
Diffusion local time storage
In this paper we study a storage process or a liquid queue in which the input
process is the local time of a positively recurrent stationary diffusion in
stationary state and the potential output takes place with a constant
deterministic rate. For this storage process we find its stationary
distribution and compute the joint distribution of the starting and ending
times of the busy and idle periods. This work completes and extends to a more
general setting the results in Mannersalo, Norros, and Salminen (2003).Comment: 24 pages; to appear in Stoch. Proc. App
On the excursions of reflected local time processes and stochastic fluid queues
This paper extends previous work by the authors. We consider the local time
process of a strong Markov process, add negative drift, and reflect it \`a la
Skorokhod. The resulting process is used to model a fluid queue. We derive an
expression for the joint law of the duration of an excursion, the maximum value
of the process on it, and the time distance between successive excursions. We
work with a properly constructed stationary version of the process. Examples
are also given in the paper.Comment: 29 pages, 4 figure
A note on a.s. finiteness of perpetual integral functionals of diffusions
In this note, with the help of the boundary classification of diffusions, we
derive a criterion of the convergence of perpetual integral functionals of
transient real-valued diffusions. In the particular case of transient Bessel
processes, we note that this criterion agrees with the one obtained via
Jeulin's convergence lemma
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