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Disambiguation of "Pitman, J. W."

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Some divergent integrals of Brownian motion

, and . Analytic and Geometric Stochastics: Papers in Honour of G. E. H. Reuter (Special supplement to Adv. App. Prob), Applied Prob. Trust, (1986)

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Matthias J W Bohnen

Andreas J W Hartel

Walter W J Döpper

Friedrich W J Fröhlig

Hendrik W J Kroes

 

Other publications of authors with the same name

One-dimensional Brownian motion and the three-dimensional Bessel process. Advances in Applied Probability, (1975)An identity for stopping times of a Markov Process. Studies in Probability and Statistics, Jerusalem Academic Press, (1974)Some divergent integrals of Brownian motion, and . Analytic and Geometric Stochastics: Papers in Honour of G. E. H. Reuter (Special supplement to Adv. App. Prob), Applied Prob. Trust, (1986)Remarks on the convex minorant of Brownian motion. Seminar on Stochastic Processes, 1982, page 219-227. Birkhäuser, Boston, (1983)On coupling of Markov chains. Z. Wahrsch. Verw. Gebiete, (1976)Brownian interpretations of an elliptic integral, , and . Seminar on Stochastic Processes, 1991, page 83-95. Birkhäuser, Boston, (1992)Quelques identités en loi pour les processus de Bessel, and . Hommage à P.A. Meyer et J. Neveu, Soc. Math. de France, (1996)Uniform rates of convergence for Markov chain transition probabilities. Z. Wahrsch. Verw. Gebiete, (1974)Lévy systems and path decompositions. Seminar on Stochastic Processes, 1981, page 79-110. Birkhäuser, Boston, (1981)Markov functions, and . Ann. Probab., 9 (4): 573--582 (1981)Let $(G,G)$ and $(H,H)$ be two measurable spaces, and $f$ be a measurable function of $G$ into $H$. If $\X(t)\$ is a homogeneous Markov process with initial distribution $łambda$ and state space $G$, under what conditions is the process $f(X(t))$ Markov? Conditions are well known for $f(X)$ to be Markov for all the initial distributions $łambda$, or invariant $łambda$. This article provides conditions for $f(X)$ to be Markov when there may be no invariant $łambda$, or for some though not all initial $łambda$. The main result is then applied to present a simple proof of Williams' result: For a linear Brownian motion $B(t)$ starting from 0 and with drift $\mu$, the process $Y(t)=2M(t)-B(t)$ (where $M(t)=B(s)\ 0st$) is a diffusion following the same law as the radial part of a three-dimensional Brownian motion starting from the origin and with drift $|\mu|$..