On Properties of the Dirichlet Green's function for linear diffusions on a half line
Analysis of PDEs
2021-03-09 v1 Optimization and Control
Probability
Abstract
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian. Formulas for the Dirichlet Green's function on the half line are only known in special cases. The main object of study in the paper is the ratio of the Dirichlet to whole line Green's functions. Bounds, asymptotic behavior in the limit as the diffusion coefficient vanishes, and a log concavity result are obtained for this ratio.
Cite
@article{arxiv.2103.03929,
title = {On Properties of the Dirichlet Green's function for linear diffusions on a half line},
author = {Joseph G. Conlon and Michael Dabkowski},
journal= {arXiv preprint arXiv:2103.03929},
year = {2021}
}
Comments
60 pages