Search results for "Diffusion approximation"

showing 3 items of 3 documents

Forward and backward diffusion approximations for haploid exchangeable population models

2001

Abstract The class of haploid population models with non-overlapping generations and fixed population size N is considered such that the family sizes ν1,…,νN within a generation are exchangeable random variables. A criterion for weak convergence in the Skorohod sense is established for a properly time- and space-scaled process counting the number of descendants forward in time. The generator A of the limit process X is constructed using the joint moments of the offspring variables ν1,…,νN. In particular, the Wright–Fisher diffusion with generator Af(x)= 1 2 x(1−x)f″(x) appears in the limit as the population size N tends to infinity if and only if the condition lim N→∞ E((ν 1 −1) 3 )/(N Var …

Exchangeable random variablesStatistics and ProbabilityDualityPopulation geneticsCoalescent theoryDiffusion approximationModelling and SimulationQuantitative Biology::Populations and EvolutionNeutralityWright–Fisher diffusionHille–Yosida theoremWeak convergenceMathematicsWeak convergenceApplied MathematicsMathematical analysisHeavy traffic approximationCommutative diagramHille–Yosida theoremPopulation modelDiffusion processModeling and SimulationAncestorsDescendantsExchangeabilityCoalescentStochastic Processes and their Applications
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M/M/1 queue in two alternating environments and its heavy traffic approximation

2018

We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating with anomalous working phases or random repairing periods. We first obtain the steady-state distribution of the process in terms of a generalized mixture of two geometric distributions. In the special case when only one kind of switch is allowed, we analyze the transient distribution, and investigate the busy period problem. The analysis is also performed by means of a suitable heavy-traffic approximation which leads to a continuous random process. Its d…

Partial differential equationMarkov chainDistribution (number theory)Stochastic processApplied MathematicsProbability (math.PR)010102 general mathematicsMathematical analysisM/M/1 queue60K25 60K37 60J60 60J70Heavy traffic approximation01 natural sciencesSteady-state distribution010104 statistics & probabilityDiffusion approximationFOS: MathematicsAlternating Wiener process0101 mathematicsFirst-hitting-time modelSteady-state distribution; First-passage time; Diffusion approximation; Alternating Wiener processQueueMathematics - ProbabilityAnalysisFirst-passage timeMathematicsJournal of Mathematical Analysis and Applications
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The coalescent in population models with time-inhomogeneous environment

2002

AbstractThe coalescent theory, well developed for the class of exchangeable population models with time-homogeneous reproduction law, is extended to a class of population models with time-inhomogeneous environment, where the population size is allowed to vary deterministically with time and where the distribution of the family sizes is allowed to change from generation to generation. A new class of time-inhomogeneous coalescent limit processes with simultaneous multiple mergers arises. Its distribution can be characterized in terms of product integrals.

Statistics and ProbabilityWeak convergencePopulation geneticsApplied MathematicsPopulation sizeVarying environmentPopulation geneticsProduct integralHeavy traffic approximationProduct integralStirling numbersCoalescent theoryFamily SizesDiffusion approximationPopulation modelAncestorsModelling and SimulationModeling and SimulationEconometricsQuantitative Biology::Populations and EvolutionCoalescentStatistical physicsWeak convergenceMathematicsStochastic Processes and their Applications
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