Large deviations for processes on half-line.(English)Zbl 1329.60055

Summary: We consider a sequence of processes $$X_n(t)$$ defined on the half-line $$0\leq t<\infty$$. We give sufficient conditions for a large deviation principle (LDP) to hold in the space of continuous functions with metric $\rho(f,g)=\sup_{t\geq0} |f(t) - g(t)|/(1+t^{1+\kappa}), \;\;\kappa\geq0.$ The LDP is established for random walks, diffusions, and the CEV model of ruin, all defined on the half-line. The LDP in this space is “more precise” than that with the usual metric of uniform convergence on compacts.

MSC:

 60F10 Large deviations 60G50 Sums of independent random variables; random walks 60J60 Diffusion processes 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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