An asymptotic formula for the semimartingale local time of reflecting Brownian motion on an interval

Authors

  • M.N. Pascu Transilvania University of Brasov, Romania
  • N.R. Pascu Southern Polytechnic State University, USA
  • O. Racheru Transilvania University of Brasov, Romania

Keywords:

reflecting Brownian motion, semimartingale local time, boundary local time, Neumann problem, Laplace operator, asymptotic behavior

Abstract

We derive an asymptotic formula for the expected value of the difference of the semimartingale local times of the 1-dimensional reflecting Brownian motion on [−1, 1] at the two ends of the interval. As an application, we derive the classical probabilistic representation of the solution of the Neumann problem for the Laplace operator in the 1-dimensional case.

Author Biographies

M.N. Pascu, Transilvania University of Brasov, Romania

Department of Mathematics and Computer Science, Str. Iuliu Maniu Nr. 50, Brasov – 500091, Romania

N.R. Pascu, Southern Polytechnic State University, USA

Department of Mathematics, 1100 S. Marietta Pkwy, Marietta, GA 30060-2896

O. Racheru, Transilvania University of Brasov, Romania

Department of Mathematics and Computer Science, Str. Iuliu Maniu Nr. 50, Brasov – 500091, Romania

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Published

2014-06-10

Issue

Vol. 7(56) No. 1 (2014)

Section

MATHEMATICS