Limit Theorems For Occupation Times Research Articles

Occupation times for age-structured branching processes

We consider occupation time processes for the age-structured branching processes with or without immigration introduced by Ji and Li (2022). Two large number laws and a central limit theorem for occupation times of the model with immigration are obtained.

A second order limit law for occupation times of the Cauchy process

The purpose of this note is to extend a second order limit law for one dimensional Cauchy process obtained in Kasahara (Y. Kasahara, Limit theorems for occupation times of Markov processes, Publ. RIMS, Kyoto Univ. 12 (1977), pp. 801–818), using the method of moments and some kind of chaining argument.

A limit theorem for occupation times of Lamperti’s stochastic processes

The arcsine law for random walks on the line is well known and it was extended greatly by Lamperti for a class of discrete-time stochastic processes. In the present paper we treat its extreme case where the excursion intervals have very heavy tail probabilities. The result is a refinement of Lamperti’s theorem. A functional limit theorem is also discussed.

Functional limit theorems for occupation times of Lamperti’s stochastic processes in discrete time

Two functional limit theorems for occupation times of Lamperti’s stochastic processes are established. One is a generalization of Lamperti’s result in 1957 in the null recurrent case, and the other is a limit theorem for the fluctuation in the positively recurrent case. The proofs are based on a limit theorem for i.i.d. random variables with common distribution function belonging to the domain of attraction of a stable law.

Occupation times of sets of infinite measure for ergodic transformations

Assume that T is a conservative ergodic measure preserving transformation of the infinite measure space (X,A,µ). We study the asymptotic behaviour of occupation times of certain subsets of infinite measure. Specifically, we prove a Darling-Kac type distributional limit theorem for occupation times of barely infinite components which are separated from the rest of the space by a set of finite measure with c.f.-mixing return process. In the same setup we show that the ratios of occupation times of two components separated in this way diverge almost everywhere. These

Théorèmes limites pour certaines fonctionnelles associées aux processus stables sur l’espace de Hölder

In this paper we study the Holder regularity property of the local time of a symmetric stable process of index 1 alt; [alpha] [less than or equal] 2 and of its fractional derivative as a doubly indexed process with respect to the space and the time variables. As an application we establish some limit theorems for occupation times of one--dimensional symmetric stable processes in the space of Holder continuous functions. Our results generalize those obtained by Fitzsimmons and Getoor for stable processes in the space on continuous functions. The limiting processes are fractional derivatives and Hilbert transforms of local times.

Functional limit theorem for occupation times of Gaussian processes---non-critical case

where X ^ X ^ , . . . are independent copies of X 7 . We shall consider only the case when fractional Brownian motion has jointly continuous local times which means the sample paths are point recurrent case, i.e., 0 2. Suppose f{x) > 0 be a bounded integrable function on M such that / := J R d f[χ)dx φ 0. We denote by lΊ^{t,x) the local time of fractional Brownian motion X 7 ' d , then putting a = 1 ηd,

A limit theorem for occupation times of fractional Brownian motion

Recently, N. Kôno gave a limit theorem for occupation times of fractional Brownian motion, which result generalizes the well-known Kallianpur-Robbins law for two-dimensional Brownian motion. This paper studies a functional limit theorem for Kôno's result. It is proved that, under a suitable normalization, the limiting process is the inverse of an extremal process.

On some limit theorems for occupation times of one dimensional Brownian motion and its continuous additive functionals locally of zero energy

On some limit theorems for occupation times of one dimensional Brownian motion and its continuous additive functionals locally of zero energy

Probability, Statistics and Analysis.

1. The asymptotic speed and shape of a particle system D. Aldous and J. Pitman 2. On doubly stochastic population processes M. S. Bartlett 3. On limit theorems for occupation times N. H. Bingham and J. Hawkes 4. The Martin boundary of two dimensional Ornstein-Uhlenbeck processes M. Cranston, S. Orey and U. Rosler 5. Green's and Dirichlet spaces for a symmetric Markov transition function E. B. Dynkin 6. On a theorem of Kabanov, Liptser and Sirjaev G. K. Eagleson and R. F. Gundy 7. Oxford Commemoration Ball J. M. Hammersley 8. Invariant measures and the q-matrix F. P. Kelly 9. The appearance of a multivariate exponential distribution in sojourn times for birth-death and diffusion processes J. T. Kent 10. Three unsolved problems in discrete Markov theory J. F. C. Kingman 11. The electrostatic capacity of an ellipsoid P. A. P. Moran 12. Stationary one-dimensional Markov random fields with a continuous state space F. Papangelou 13. A uniform central limit theorem for partial-sum processes indexed by sets R. Pyke 14. Multidimensional randomness B. D. Ripley 15. Some properties of a test for multimodality based on kernel density estimates B. W. Silverman 16. Criteria for rates of convergence of Markov chains, with application to queueing and storage theory R. L. Tweedie 17. Competition and bottle-necks P. Whittle.

Two limit Theorems for occupation times of Markov processes

Two limit Theorems for occupation times of Markov processes

Limit theorems for occupation times of Markov processes

Limit theorems for occupation times of Markov processes