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Diffusion Processes and their Sample Paths Henry P. Jr. McKean, Kiyosi Itô
Publisher: Springer Berlin Heidelberg

As a result, this branching diffusion. Such results lead to sample path LDP for the price process in the Heston and Hull & White Portfolios and risk premia converge to their long-run counterparts as the horizon becomes large. Formulas of interest rate path dependent options when the dynamics of the underlying asset Diffusion Processes and their Sample Paths. Academic Press, New York and Springer-Verlag, Berlin, 1965. Mc KEAN, JR., Diffusion Processes and their Sample Paths,. Regular strong Markov process with continuous sampling paths and time- stationary fully characterized by its coefficients under the regularity conditions. P., Diffusion Processes and their Sample Paths (Springer, Berlin, 1965). Motivated by path-integral numerical solutions of diffusion processes, PATHINT, we present There are three equivalent mathematical representations of a diffusion process, provided of course . Diffusion processes are characterized by the continuity of their sample paths. For example, for the upper branch case,. Since the Friedlin-Wentzell LDP results do not hold in the Heston model, sample path LDP are derived for a class of diffusion processes allowed to have a non-locally Lipschitz diffusion matrix. Diffusion processes from discretely sampled observations. For this supercritical binary branching diffusion process, there is a tradeoff between branching events giving birth to new particles and absorption at the boundaries, killing the particles. Roughly speaking, the transformation of paths procedure allows to select sample paths of the original process with, say, a fixed destination and/or, more generally, to kill certain sample paths that do not fit the integral criterion encoded by the additive functional.