Pinned diffusions and Markov bridges

2017/11/23 by Hildebrandt, Florian, Rœlly, Sylvie · 2 citations
#60G15 #60H10 #60J60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1711.08617

Abstract

In this article we consider a family of real-valued diffusion processes on the time interval [0,1] indexed by their prescribed initial value x ∈ ℝ and another point in space, y ∈ ℝ. We first present an easy-to-check condition on their drift and diffusion coefficients ensuring that the diffusion is pinned in y at time t=1. Our main result then concerns the following question: can this family of pinned diffusions be obtained as the bridges either of a Gaussian Markov process or of an Itô diffusion? We eventually illustrate our precise answer with several examples.

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