Time Reversal of Diffusions

Continuous Time Perpetuities and the Time Reversal of Diffusions

Time Reversal of Diffusions' by U. G. Haussmann And

It is shown that if a diffusion process, {Xt: 0 < t < 1}, on Rd satisfies dXt = b(t, Xt) dt + a(t, Xt) dwt then the reversed process, {Xt: 0 < t < 1} where Xt = Xl t , is again a diffusion with drift b and diffusion coefficient a, provided some mild conditions on b, a, and p(, the density of the law of X(, hold. Moreover b and a are identified. 1. Introduction. It is well known that a Markov pr...

Reverse Time Diffusions

This paper is a continuation of work commenced in [l] and considers a diffusion in R" given as the solution of a family of stochastic differential equations. The problem discussed is to suppose the direction of the time parameter is reversed, that is, time evolves in anegative direction and the same diffusion process is observed, with the filtration generated by the reversed process. There is a...

Can Time-homogeneous Diffusions Produce Any Distribution?

Given a centred distribution, can one find a time-homogeneous martingale diffusion starting at zero which has the given law at time 1? We answer the question affirmatively if generalized diffusions are allowed.

Semiparametric Estimation for Time-Inhomogeneous Diffusions

We develop two likelihood based approaches to semiparametrically estimate the time-inhomogeneous diffusion process: log penalized splines (P-splines) and the local log-linear method. Positive volatility is naturally embedded and this positivity is not guaranteed in most existing diffusion models. We investigate different smoothing parameter selection methods. Separate bandwidths are used for dr...