Time-Homogeneous Diffusions with a Given Marginal at a Random Time
Probability
2009-12-10 v1
Abstract
We solve explicitly the following problem: for a given probability measure mu, we specify a generalised martingale diffusion X which, stopped at an independent exponential time T, is distributed according to mu. The process X is specified via its speed measure m. We present three proofs. First we show how the result can be derived from the solution of Bertoin and Le Jan (1992) to the Skorokhod embedding problem. Secondly, we give a proof exploiting applications of Krein's spectral theory of strings to the study of linear diffusions. Finally, we present a novel direct probabilistic proof based on a coupling argument.
Cite
@article{arxiv.0912.1719,
title = {Time-Homogeneous Diffusions with a Given Marginal at a Random Time},
author = {Alexander M. G. Cox and David G. Hobson and Jan K. Obłój},
journal= {arXiv preprint arXiv:0912.1719},
year = {2009}
}
Comments
15 pages, 2 figures