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Levy Processes with...
Levy Processes with Two-Sided Reflection
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Andersen, Lars Norvang (författare)
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Asmussen, Soren (författare)
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Glynn, Peter W. (författare)
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- Pihlsgård, Mats (författare)
- Lund University,Lunds universitet,Geriatrik,Forskargrupper vid Lunds universitet,Geriatric Medicine,Lund University Research Groups,Geriatrics
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(creator_code:org_t)
- Cham : Springer International Publishing, 2015
- 2015
- Engelska.
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Ingår i: Lecture Notes in Mathematics. - Cham : Springer International Publishing. - 0075-8434. ; 2149, s. 67-182
- Relaterad länk:
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http://dx.doi.org/10...
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https://lup.lub.lu.s...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- Let X be a Levy process and V the reflection at boundaries 0 and b > 0. A number of properties of V are studied, with particular emphasis on the behaviour at the upper boundary b. The process V can be represented as solution of a Skorokhod problem V(t) = V(0)+X(t)+L(t)-U(t) where L, U are the local times (regulators) at the lower and upper barrier. Explicit forms of V in terms of X are surveyed as well as more pragmatic approaches to the construction of V, and the stationary distribution pi is characterised in terms of a two-barrier first passage problem. A key quantity in applications is the loss rate l(b) at b, defined as E-pi U(1). Various forms of l(b) and various derivations are presented, and the asymptotics as b -> infinity is exhibited in both the light-tailed and the heavy-tailed regime. The drift zero case EX(1) = 0 plays a particular role, with Brownian or stable functional limits being a key tool. Further topics include studies of the first hitting time of b, central limit theorems and large deviations results for U, and a number of explicit calculations for Levy processes where the jump part is compound Poisson with phase-type jumps.
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- Applied probability
- Central limit theorem
- Finite buffer problem
- First
- passage problem
- Functional limit theorem
- Heavy tails
- Integro-differential equation
- Ito's formula
- Linear equations
- Local
- time
- Loss rate
- Martingale
- Overflow
- Phase-type distribution
- Poisson's equation
- Queueing theory
- Siegmund duality
- Skorokhod
- problem
- Storage process
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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