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On moments of the integrated exponential Brownian motion

Caravelli, F; Mansour, T; Sindoni, L; Severini, S; (2016) On moments of the integrated exponential Brownian motion. European Physical Journal Plus , 131 (245) 10.1140/epjp/i2016-16245-9. Green open access

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Abstract

We present new exact expressions for a class of moments for the geometric Brownian motion, in terms of determinants, obtained using a recurrence relation and combinatorial arguments for the case of a Ito's Wiener process. We then apply the obtained exact formulas to computing averages of the solution of the logistic stochastic differential equation via a series expansion, and compare the results to the solution obtained via Monte Carlo.

Type: Article
Title: On moments of the integrated exponential Brownian motion
Open access status: An open access version is available from UCL Discovery
DOI: 10.1140/epjp/i2016-16245-9
Publisher version: http://dx.doi.org/10.1140/epjp/i2016-16245-9
Language: English
Additional information: Open Access. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords: cond-mat.stat-mech, cond-mat.stat-mech, math-ph, math.MP
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/1505288
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