On sequences of martingales with jumps on Riemannian submanifolds

Autor:	Okazaki, Fumiya
Rok vydání:	2024
Předmět:	Mathematics - Probability 60G44 60H05
Druh dokumentu:	Working Paper
Popis:	In this article, we investigate sequences of discontinuous martingales on submanifolds of higher-dimensional Euclidean space. Those sequences naturally arise when we deal with a sequence of harmonic maps with respect to non-local Dirichlet forms, such as fractional harmonic maps. We prove that the semimartingale topology is equivalent to the topology of locally uniform convergence in probability on the space of discontinuous martingales on manifolds. In particular, we show that the limit of any sequence of discontinuous martingales on a compact Riemannian manifold, with respect to the topology of locally uniform convergence in probability, is a martingale on the manifold. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.17118 Zobrazit plný text záznamu View this record from Arxiv