5 papers
Exact moduli of continuity for the local times of Feller Brownian motions
P. J. Fitzsimmons, Jay Rosen
We examine the modulus of continuity, in the spatial variable, of the local time process of Feller Brownian motion (FBM) on the half-line . Briefly, a FBM is a strong M…
Ray-Knight theorems for the local times of rebirthed Markov processes
P. J. Fitzsimmons, Jay Rosen
We prove generalizations of the first and second Ray-Knight theorems, for a large class of non-symmetric strong Markov processes. These results link the local times of the Markov p…
Kemeny's Constant for Markov Processes
P. J. Fitzsimmons
The mean time taken by an irreducible Markov chain on a finite state space to hit a target chosen at random according to the stationary distribution does not depend on the initial…
A Peculiar Proof of the Martingale Convergence Theorem
P. J. Fitzsimmons
We prove the Martingale Convergence Theorem by using the work of L. Dubins and I. Monroe about embedding a given discrete-time martingale in the sample paths of a Brownian motion.
Moduli of continuity for the local times of rebirthed Markov processes
P. J. Fitzsimmons, Michael B. Marcus, Jay Rosen
Let a be locally compact space with a countable base. Let be a transient symmetric Borel right process with state space and continuous strictly positive --poten…