60 citations · 104 across the 9 of their papers we have counts for
9 papers
A Proof of Lehoczky's Theorem on Drawdowns
P. J. Fitzsimmons
We give a proof of Lehoczky's drawdown formula for one-dimensional diffusion processes, using the Poisson structure of the excursions of the diffusion below its running maximum.
On a Proof of the Strong Law of Large Numbers
Patrick J. Fitzsimmons
Inspired by a recent preprint of N. Curien, we provided what may be a new and elementary proof of the Law of Large Numbers.
On the Dirichlet form of three-dimensional Brownian motion conditioned to hit the origin
Patrick J. Fitzsimmons, Liping Li
Our concern in this paper is the energy form induced by an eigenfunction of a self-adjoint extension of the restriction of the Laplace operator to $C_c^\infty(\mathbf{R}^3\setminus…
Excursions Above the Minimum for Diffusions
P. J. Fitzsimmons
We demonstrate the existence of a "Lévy system" for the excursions of a one-dimensional diffusion process above its past-minimum process. As applications we provide a direct proof…
Errata for Stochastic calculus for symmetric Markov processes
Zhen-Qing Chen, Patrick J. Fitzsimmons, Kazuhiro Kuwae +1
This erratum corrects the article arXiv:0806.2044 published in Ann. Probab. 36 (2008) 931--970
Stochastic calculus for symmetric Markov processes
Z. -Q. Chen, P. J. Fitzsimmons, K. Kuwae +1
Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties o…