On explicit solutions to Ito diffusions
Probability
2016-09-13 v3
Abstract
Strong solutions of p-dimensional stochastic differential equations that can be represented locally in explicit simulation form are considered. The following three-way equivalence is established: 1) There exists such a representation from all starting points, 2) the representation pair satisfies a set differential equations, and 3) the stochastic differential equation coefficients satisfy commutation relations. Next, construction theorems, based on a diffeomorphism between the original equation solutions and the strong solutions to a simpler Ito integral equation, with a possible deterministic component, are given. Finally, motivating examples are provided and reference to its importance in filtering and option pricing is given.
Keywords
Cite
@article{arxiv.1608.05362,
title = {On explicit solutions to Ito diffusions},
author = {Michael A. Kouritzin and Bruno Remillard},
journal= {arXiv preprint arXiv:1608.05362},
year = {2016}
}
Comments
27 pages