Area Distribution of Elastic Brownian Motion

Details Area Distribution of Elastic Brownian Motion Area Distribution of Elastic Brownian Motion

2009-06-17

arxiv.org/abs/0906.3262v2

J. Phys. A: Math. Theor. 42 (2009) 485205

Physics

Condensed Matter

Statistical Mechanics

18 pages, published version

Scientific paper

We calculate the excursion and meander area distributions of the elastic Brownian motion by using the self adjoint extension of the Hamiltonian of the free quantum particle on the half line. We also give some comments on the area of the Brownian motion bridge on the real line with the origin removed. We will stress on the power of self adjoint extension to investigate different possible boundary conditions for the stochastic processes.

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