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We present a list of equivalent expressions and extensions of Bougerols celebrated identity in law, obtained by several authors. We recall well-known results and the latest progress of the research associated with this celebrated identity in many directions, we give some new results and possible extensions and we try to point out open questions.
We prove a version of the classical Dufresne identity for matrix processes. In particular, we show that the inverse Wishart laws on the space of positive definite r x r matrices can be realized by the infinite time horizon integral of M_t times its t
We prove an identity in distribution between two kinds of partition functions for the log-gamma directed polymer model: (1) the point-to-point partition function in a quadrant, (2) the point-to-line partition function in an octant. As an application,
Using a divergent Bass-Burdzy flow we construct a self-repelling one-dimensional diffusion. Heuristically, it can be interpreted as a solution to an SDE with a singular drift involving a derivative of the local time. We show that this self-repelling
A bootstrap percolation process on a graph $G$ is an infection process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours becomes infect
In this paper we investigate the well-posedness of backward or forward stochastic differential equations whose law is constrained to live in an a priori given (smooth enough) set and which is reflected along the corresponding normal vector. We also s