Markovian bridges and reversible diffusion processes with jumps
Markovian bridges driven by Lévy processes are constructed from the data of an initial and final distribution, as particular cases of a family of time reversible diffusions with jumps. In this way a large class of not necessarily continuous Markovian Bernstein processes are constructed. These processes are also characterized by using the theory of stochastic control for jump processes. The construction is motivated by Euclidean quantum mechanics in momentum representation, but the resulting class of processes is much bigger than the one needed for this purpose. The paper also includes a large collection of examples.
scientific article; zbMATH DE number 2107311
scientific article