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Thilanka Appuhamillage

Publications and source records attributed to Thilanka Appuhamillage.

3 recordsLinked to original sources
arXiv2012

Interfacial Phenomena and Natural Local Time

This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments of recent experiments and observations of phenomena in the geophysical and biological sciences pertaining to dispersion in the presence of an interface of discontinuity in dispersion coefficients. The results illustrate new ways in which to use the theory of stochastic processes to infer macro scale parameters and behavior from micro scale observations in particular heterogeneous environments.

math.PR↗
arXiv2012

Corrections for "Occupation and local times for skew Brownian motion with applications to dispersion across an interface"

We are making corrections and acknowledging colleagues that pointed out mistakes in our recent paper titled "Occupation and local times for skew Brownian motion with applications to dispersion across an interface" which was published in Annals of Applied Probability (2011) 21(1) 183-214. Specifically the corrections are: 1. The restriction of $γ$ to non negative values in Theorem 1.3 is not needed. But one has probabilistic interpretation only when $γ$ is non negative. 2. State the correct formulas in Corollary 3.3 as their were computational errors in the original formulas. We thank Pierre Etoiré and Miguel Martinez for pointing out these errors.

math.PR↗
arXiv2011

First Passage Time of Skew Brownian Motion

Nearly fifty years after the introduction of skew Brownian motion by Itô and McKean (1963), the first passage time distribution remains unknown. In this paper, we generalize results of Pitman and Yor (2001) and Csáki and Hu (2004) to derive formulae for the distribution of ranked excursion heights of skew Brownian motion. We then derive the first passage time distribution as a simple corollary.

math.PR↗