English

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