Convergence of Martingales with Jumps on Submanifolds of Euclidean Spaces and its Applications to Harmonic Maps

Fumiya Okazaki ()
Additional contact information
Fumiya Okazaki: Tohoku University

Journal of Theoretical Probability, 2024, vol. 37, issue 2, 1168-1198

Abstract: Abstract Martingales with jumps on Riemannian manifolds and harmonic maps with respect to Markov processes are discussed in this paper. Discontinuous martingales on manifolds were introduced in Picard (Séminaire de Probabilités de Strasbourg 25:196–219, 1991). We obtain results about the convergence of martingales with finite quadratic variations on Riemannian submanifolds of higher-dimensional Euclidean space as $$t\rightarrow \infty $$ t → ∞ and as $$t\rightarrow 0$$ t → 0 . Furthermore, we apply the result about martingales with jumps on submanifolds to harmonic maps with respect to Markov processes such as fractional harmonic maps.

Keywords: Manifold-valued martingales; Stochastic calculus on manifolds; Harmonic maps; Jump process; 60G44; 60J45 (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-023-01273-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:37:y:2024:i:2:d:10.1007_s10959-023-01273-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-023-01273-6

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().