Open Access
2015 Large deviations for processes on half-line
Fima Klebaner, Artem Logachev, Anatoli Mogulski
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Electron. Commun. Probab. 20: 1-14 (2015). DOI: 10.1214/ECP.v20-4130


We consider a sequence of processes X_n(t)$ defined on half-line $0\leq t<\infty$. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with metric $\rho(f,g)=\sup_{t\geq0} |f(t)−g(t)|/(1+t^{1+\kappa})$, $\kappa\geq0$. LDP is established for Random Walks, Diffusions, and CEV model of ruin, all defined on the half-line. LDP in this space is "more precise" than that with the usual metric of uniform convergence on compacts.


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Fima Klebaner. Artem Logachev. Anatoli Mogulski. "Large deviations for processes on half-line." Electron. Commun. Probab. 20 1 - 14, 2015.


Accepted: 24 October 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60055
MathSciNet: MR3417447
Digital Object Identifier: 10.1214/ECP.v20-4130

Primary: 60F10
Secondary: 60G50 , 60H10 , 60J60

Keywords: CEV model , Diffusion processes , large deviations , Random walk

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