Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T17:49:09.365Z Has data issue: false hasContentIssue false
  • English
  • Français

Recurrence for Markov processes on N lines

Published online by Cambridge University Press:  14 July 2016

Mark Pinsky
Mark Pinsky*
Affiliation:
Northwestern University, Evanston, Illinois
Get accessRights & Permissions [Opens in a new window]

Extract

Let Λ = R 1 × {1, 2, ···, N} denote N copies of the real line and ξ(t) = (X(t), α(t))be a right-continuous Markov process taking values in A having transition function of the form P(t, (x, α), A × {β}) = Fαβ (t, A – x). Fukushima and Hitsuda [2] have found the most general such transition function; the (matrix) logarithm of its characteristic function is decomposed into a Lévy-Khintchine integral on the diagonal and multiples of characteristic functions off the diagonal.

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971, pp. 724 - 730
Copyright
Copyright © Applied Probability Trust 1971 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Dynkin, E. B. (1965) Markov Processes. Academic Press, New York.Google Scholar
[2] Fukushima, M. and Hitsuda, M. (1967) On a class of Markov processes taking values on lines and the central limit theorem. Nagoya Math. J. 30, 7–56.CrossRefGoogle Scholar
[3] Hersh, R. and Pinsky, M. (1971) Random evolutions are asymptotically Gaussian. Comm. Pure Appl. Math. (To appear).CrossRefGoogle Scholar
[4] Hitsuda, M. and Shimizu, A. (1970) The central limit theorem for additive functionals of Markov processes and the weak convergence to Wiener measure. J. Math. Soc. Japan 22, 551–566.Google Scholar
[5] Ito, K. (1959) Lectures on Stochastic Processes. Tata Institute Bombay.Google Scholar
[6] Pinsky, M. (1968) Differential equations with a small parameter and the central limit theorem for functions defined on a finite Markov chain. Z. Wahrscheinlichkeitsth. 9, 101–111.Google Scholar