M A Rajabpour 2009 J. Phys. A: Math. Theor. 42 485205 doi:10.1088/1751-8113/42/48/485205
Area distribution of an elastic Brownian motion
M A Rajabpour
Show affiliationsWe 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 focus on the power of self-adjoint extension to investigate different possible boundary conditions for the stochastic processes. We also discuss some possible physical applications.
- PACS
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03.65.Db Functional analytical methods
03.65.Vf Phases: geometric; dynamic or topological
02.60.Lj Ordinary and partial differential equations; boundary value problems
- MSC
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60G20 Generalized stochastic processes
81P20 Stochastic mechanics (including stochastic electrodynamics)
60J65 Brownian motion (See also 58J65)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
- Subjects
- Dates
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Issue 48 (4 December 2009)
Received 17 June 2009, in final form 20 September 2009
Published 12 November 2009
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Area distribution of an elastic Brownian motion
M A Rajabpour 2009 J. Phys. A: Math. Theor. 42 485205
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