On moments of the integrated exponential Brownian motion
arXiv:1509.05980
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.
11 pages, 3 figures - accepted for publication on EPJ Plus