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On an ergodic property of a certain class of Markov processes
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kallianpur, Gopinath |
| Copyright Year | 1955 |
| Abstract | and (1.6) For fixed u, p(t, u) is a continuous function of t for t different from zero. The above conditions on the transition function are suggested by applications to the Brownian motion and, in the discrete case, to sums of independent random variables belonging to the domain of attraction of symmetric stable laws. There are Markov processes besides the Brownian motion for which conditions (1.1) to (1.6) are fulfilled, e.g. the Cauchy process with p(t, u) = t7r1l(t2 + u2)-. The main object of this paper is to prove an ergodic or "equidistribution" property of the Brownian motion process, a weak form of |
| Starting Page | 159 |
| Ending Page | 169 |
| Page Count | 11 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-1955-0069420-4 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/1955-006-02/S0002-9939-1955-0069420-4/S0002-9939-1955-0069420-4.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-1955-0069420-4 |
| Volume Number | 6 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
