62,573 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
GMT/local-time conversion chart
GMT/local-time conversion is made by a longitude pocket instrument that automatically indicates desired information by simply manipulating the moveable portion of the instrument in accordance with a set of simple instructions imprinted on the reverse side of the instrument
Interfacial Phenomena and Natural Local Time
This article addresses a modification of local time for stochastic processes,
to be referred to as `natural local time'. It is prompted by theoretical
developments arising in mathematical treatments of recent experiments and
observations of phenomena in the geophysical and biological sciences pertaining
to dispersion in the presence of an interface of discontinuity in dispersion
coefficients. The results illustrate new ways in which to use the theory of
stochastic processes to infer macro scale parameters and behavior from micro
scale observations in particular heterogeneous environments
Continuity of Local Time: An applied perspective
Continuity of local time for Brownian motion ranks among the most notable
mathematical results in the theory of stochastic processes. This article
addresses its implications from the point of view of applications. In
particular an extension of previous results on an explicit role of continuity
of (natural) local time is obtained for applications to recent classes of
problems in physics, biology and finance involving discontinuities in a
dispersion coefficient. The main theorem and its corollary provide physical
principles that relate macro scale continuity of deterministic quantities to
micro scale continuity of the (stochastic) local time.Comment: To appear in: "The fascination of Probability, Statistics and Their
Applications. In honour of Ole E. Barndorff-Nielsen on his 80th birthday
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