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.


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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