B S, Balakrishna (2013): On multi-particle Brownian survivals and the spherical Laplacian.
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Abstract
The probability density function for survivals, that is for transitions without hitting a barrier, for a collection of particles driven by correlated Brownian motions is analyzed. The analysis is known to lead to a study of the spectrum of the Laplacian on domains on the sphere in higher dimensions. The first eigenvalue of the Laplacian governs the large time behavior of the probability density function and the asymptotics of the hitting time distribution. It is found that the solution leads naturally to a spectral function, a `generating function' for the eigenvalues and multiplicities of the Laplacian. Analytical properties of the spectral function suggest a simple scaling procedure for determining the eigenvalues, readily applicable for a homogeneous collection of correlated particles. Comparison of the first eigenvalue with the available theoretical and numerical results for some specific domains shows remarkable agreement.
Item Type: | MPRA Paper |
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Original Title: | On multi-particle Brownian survivals and the spherical Laplacian |
Language: | English |
Keywords: | Brownian; Survival Probability; Hitting Time; Correlation; Laplacian; Spherical Domain; Eigenvalue |
Subjects: | C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing |
Item ID: | 44459 |
Depositing User: | S Balakrishna |
Date Deposited: | 18 Feb 2013 15:11 |
Last Modified: | 27 Sep 2019 16:53 |
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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/44459 |
Available Versions of this Item
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On multi-particle Brownian survivals and the spherical Laplacian. (deposited 04 Jan 2013 16:49)
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On multi-particle Brownian survivals and the spherical Laplacian. (deposited 25 Jan 2013 13:46)
- On multi-particle Brownian survivals and the spherical Laplacian. (deposited 18 Feb 2013 15:11) [Currently Displayed]
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On multi-particle Brownian survivals and the spherical Laplacian. (deposited 25 Jan 2013 13:46)