Convergence of martingales with jumps on manifolds and its applications to harmonic maps

Fumiya Okazaki

Published 2021-05-19Version 1

Martingales with jumps on Riemannian manifolds are discussed in this paper. They were introduced in Picard (1991). We obtain some results about the convergence of martingales with integrable quadratic variations on Riemannian manifolds. Our results include martingales whose jumps are not given by an exponential map. We apply the results to harmonic maps valued in submanifolds with respect to jump diffusions such as fractional harmonic maps.