Pinned diffusions and Markov bridges

Autoren: Florian Hildebrandt, Sylvie Roelly (2020)

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

Journal of Theoretical Probability

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