Time homogeneous diffusions with a given marginal at a deterministic time
2013 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, Vol. 123, no 3, 675-718 p.Article in journal (Refereed) Published
In this article, it is proved that for any probability law μ over R with finite first moment and a given deterministic time t>0, there exists a gap diffusion with law μ at the prescribed time t.
The method starts by constructing a discrete time process X on a finite state space, where Xτ has law μ, for a geometric time τ, independent of the diffusion. This argument is developed, using a fixed point theorem, to give conditions for the existence of a process with prescribed law when stopped at an independent time with negative binomial distribution. Reducing the time mesh gives a continuous time diffusion with prescribed law for τ with Gamma distribution. Keeping E[τ]=t fixed, the parameters of the Gamma distribution are altered, giving the prescribed law for the deterministic time. An approximating sequence establishes the result for arbitrary probability measure over R.
Place, publisher, year, edition, pages
Elsevier, 2013. Vol. 123, no 3, 675-718 p.
Martingale diffusion, Krei˘n strings, Marginal distribution
IdentifiersURN: urn:nbn:se:liu:diva-86250DOI: 10.1016/j.spa.2012.11.008OAI: oai:DiVA.org:liu-86250DiVA: diva2:576038