Time homogeneous diffusion with drift and killing to meet a given marginal

John M. Noble

Stochastic Processes and their Applications, 2015, vol. 125, issue 4, 1500-1540

Abstract: In this article, it is proved that for any probability law μ over R and a drift field b:R→R and killing field k:R→R+ which satisfy hypotheses stated in the article and a given terminal time t>0, there exists a string m, an α∈(0,1], an initial condition x0∈R and a process X with infinitesimal generator (12∂2∂m∂x+b∂∂m−∂K∂m) where k=∂K∂x such that for any Borel set B∈B(R), P(Xt∈B|X0=x0)=αμ(B). Firstly, it is shown the problem with drift and without killing can be accommodated, after a simple co-ordinate change, entirely by the proof in Noble (2013). The killing field presents additional problems and the proofs follow the lines of Noble (2013) with additional arguments.

Keywords: Time homogeneous gap diffusion; Drift; Killing; Krei˘n strings; Marginal distribution (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spa.2014.11.006

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