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ONE DIMENSIONAL BROWNIAN MOTION WITH HOLDING AND JUMPING BOUNDARY
  • Yuk Leung
Yuk Leung
University of Delaware
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Abstract

Let a particle start at some point in the unit interval I := [0, 1] and undergo Brownian motion in I until it hits one of the end points. At this instant the particle stays put for a finite holding time with an exponential distribution and then jumps back to a point inside I with a probability density μ0 or μ1 parametrized by the boundary point it was from. The process starts afresh. The same evolution repeats independently each time. Many probabilistic aspects of this diffusion process are investigated in the paper [10]. The authors in the cited paper call this process diffusion with holding and jumping (DHJ). Our simple aim in this paper is to analyze the eigenvalues of a nonlocal boundary problem arising from this process.
04 Jan 2022Submitted to Mathematical Methods in the Applied Sciences
05 Jan 2022Assigned to Editor
05 Jan 2022Submission Checks Completed
13 Jan 2022Reviewer(s) Assigned
13 May 2022Review(s) Completed, Editorial Evaluation Pending
14 May 2022Editorial Decision: Accept
23 Jun 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8493