Stochastic optimal transport with free end time

We consider a stochastic transportation problem between two prescribed probability distributions (a source and target) over processes with general drift dependence free end times. First, in order to establish dual principle, we associate equivalent formulations of the primal guarantee its convexity lower semi-continuity respect target distributions. exhibit an Eulerian formulation, whose variational principle is given by Hamilton–Jacobi–Bellman type inequalities. In case where bounded, regularity results on minimizers then enable us prove attainment corresponding problem. also address when component cost defining Lagrangian L superlinear L≈|u|p 1<p<2, which setting reminiscent our approach – previous work deterministic controlled transport problems time. finally criteria under optimal stopping time are unique, namely strict monotonicity Lagrangian.