The Beneš equation and stochastic calculus of variations

L. Decreusefond; A. S. Üstünel

doi:10.1016/0304-4149(94)00058-2

The Beneš equation and stochastic calculus of variations

L. Decreusefond
, A. S. Üstünel

Telecom Paris

Research output: Contribution to journal › Article › peer-review

Abstract

We focus our attention on the Beneš equation which describes the behavior of the virtual waiting time in the most general single queue. Using the reflection theory and the stochastic calculus of variations, we derive new results on this equation. In particular, we give a criterion on the input stream under which the solution has an absolutely continuous law with respect to the Lebesgue measure.

Original language	English
Pages (from-to)	273-284
Number of pages	12
Journal	Stochastic Processes and their Applications
Volume	57
Issue number	2
DOIs	https://doi.org/10.1016/0304-4149(94)00058-2
Publication status	Published - 1 Jan 1995

Keywords

Beneš equation
Malliavin calculus
Reflection Theory

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10.1016/0304-4149(94)00058-2

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title = "The Bene{\v s} equation and stochastic calculus of variations",

abstract = "We focus our attention on the Bene{\v s} equation which describes the behavior of the virtual waiting time in the most general single queue. Using the reflection theory and the stochastic calculus of variations, we derive new results on this equation. In particular, we give a criterion on the input stream under which the solution has an absolutely continuous law with respect to the Lebesgue measure.",

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author = "L. Decreusefond and {\"U}st{\"u}nel, \{A. S.\}",

year = "1995",

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AU - Üstünel, A. S.

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AB - We focus our attention on the Beneš equation which describes the behavior of the virtual waiting time in the most general single queue. Using the reflection theory and the stochastic calculus of variations, we derive new results on this equation. In particular, we give a criterion on the input stream under which the solution has an absolutely continuous law with respect to the Lebesgue measure.

KW - Beneš equation

KW - Malliavin calculus

KW - Reflection Theory

U2 - 10.1016/0304-4149(94)00058-2

DO - 10.1016/0304-4149(94)00058-2

M3 - Article

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VL - 57

SP - 273

EP - 284

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

The Beneš equation and stochastic calculus of variations

Abstract

Keywords

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