Asymptotics for Hitting Times
نویسندگان
چکیده
In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class (A) F = F is continuous and concave; F (t) ≤ t for t ≥ 0.. Note that all possible asymptotics are absolutely continuous.
منابع مشابه
An Orthogonal-Polynomial Approach to First-Hitting Times of Birth–Death Processes
In a recent paper in this journal, Gong, Mao and Zhang, using the theory of Dirichlet forms, extendedKarlin andMcGregor’s classical results on first-hitting times of a birth–death process on the nonnegative integers by establishing a representation for the Laplace transform E[esTi j ] of the first-hitting time Ti j for any pair of states i and j , as well as asymptotics for E[esTi j ] when eith...
متن کاملHitting Times for Random Walks with Restarts
The time it takes a random walker in a lattice to reach the origin from another vertex x, has infinite mean. If the walker can restart the walk at x at will, then the minimum expected hitting time γ(x, 0) (minimized over restarting strategies) is finite; it was called the “grade” of x by Dumitriu, Tetali and Winkler. They showed that, in a more general setting, the grade (a variant of the “Gitt...
متن کاملCorrelation Decay and Recurrence Asymptotics for Some Robust Nonuniformly Hyperbolic Maps
Abstract. We study decay of correlations, the asymptotic distribution of hitting times and fluctuations of the return times for a robust class of multidimensional non-uniformly hyperbolic transformations. Oliveira and Viana [15] proved that there is a unique equilibrium state μ for a large class of nonuniformly expanding transformations and Hölder continuous potentials with small variation. For...
متن کاملAsymptotics for the infinite time ruin probability of a dependent risk model with a constant interest rate and dominatedly varying-tailed claim sizes
This paper mainly considers a nonstandard risk model with a constant interest rate, where both the claim sizes and the inter-arrival times follow some certain dependence structures. When the claim sizes are dominatedly varying-tailed, asymptotics for the infinite time ruin probability of the above dependent risk model have been given.
متن کاملAsymptotics of rare events in birth–death processes bypassing the exact solutions
We investigate the near-continuum asymptotics of mean first passage times in some one-variable birth–death processes. The particular problem we address is how to extract mean first passage times in the near-continuum limit from their defining finite-difference equations alone. For the simple class of processes we consider here, exact closed-form solutions for the mean first passage time between...
متن کامل