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

Klebaner, Fima C.; Logachev, Artem V.; Mogulski, Anatoli A.

Electron. Commun. Probab. 20, Paper No. 75, 14 p. (2015).

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)

Keywords:

large deviations; random walks; diffusion processes; CEV ruin model