On moments of the integrated exponential Brownian motion
Statistical Mechanics
2022-09-13 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1509.05980,
title = {On moments of the integrated exponential Brownian motion},
author = {Francesco Caravelli and Toufik Mansour and Lorenzo Sindoni and Simone Severini},
journal= {arXiv preprint arXiv:1509.05980},
year = {2022}
}
Comments
11 pages, 3 figures - accepted for publication on EPJ Plus