Reminiscences of some of Paul Lévy’s ideas in Brownian motion and in Markov chains. (English) Zbl 0677.60002

Chung, Kai Lai

Stochastic processes, Proc. 8th Semin., Gainesville/Florida 1988, Prog. Probab. 17, 99-107 (1989).

[For the entire collection see Zbl 0659.00010.]
This historical and mathematical essay is based not only on Lévy’s works, but also on the author’s corresponding previous activities. The following problems are considered:
The paths in a general Markov chain, an example of a Markov chain with only stable states and no jumps at all, discontinuities being of the second kind, excursions of a Brownian motion, a resemblance of the Brownian motion to a Markov chain with a single sticky recurrent boundary, the Brownian motion recovered as a Poisson point process run by the local clock (“mesure du voisinage”, local time). The polemic against the criticism of the lecture being the basis of this paper is added.

Reviewer: P.Froněk

MSC:

60-03	History of probability theory
01A60	History of mathematics in the 20th century
60G05	Foundations of stochastic processes

Keywords:

excursions of a Brownian motion; sticky recurrent boundary

Citations:

Zbl 0659.00010