Electronic Journal of Probability

Some norm estimates for semimartingales

Triet Pham and Jianfeng Zhang

Full-text: Open access

Abstract

In this paper we introduce a new type of norms for semimartingales, under both linear and nonlinear expectations. Our norm is defined in the spirit of  quasimartingales, and it characterizes square integrable semimartingales. This work is motivated by our study of zero-sum stochastic differential games, whose value process is conjectured to be a semimartingale under a class of probability measures.  As a by product, we establish some a priori estimates for doubly reflected BSDEs without imposing  the  Mokobodski's condition directly.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 109, 25 pp.

Dates
Accepted: 30 December 2013
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064334

Digital Object Identifier
doi:10.1214/EJP.v18-2406

Mathematical Reviews number (MathSciNet)
MR3151729

Zentralblatt MATH identifier
1288.60054

Subjects
Primary: 60G46: Martingales and classical analysis
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
Semimartingale quasimartingale $G$-expectation second order backward SDEs doubly reflected backward SDEs Doob-Meyer decompostition

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Pham, Triet; Zhang, Jianfeng. Some norm estimates for semimartingales. Electron. J. Probab. 18 (2013), paper no. 109, 25 pp. doi:10.1214/EJP.v18-2406. https://projecteuclid.org/euclid.ejp/1465064334


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