Electronic Communications in Probability

Product space for two processes with independent increments under nonlinear expectations

Qiang Gao, Mingshang Hu, Xiaojun Ji, and Guomin Liu

Full-text: Open access

Abstract

In this paper, we consider the product space for two processes with independent increments under nonlinear expectations. By introducing a discretization method, we construct a nonlinear expectation under which the given two processes can be seen as a new process with independent increments.

Article information

Source
Electron. Commun. Probab. Volume 22 (2017), paper no. 11, 12 pp.

Dates
Received: 7 March 2016
Accepted: 17 January 2017
First available in Project Euclid: 26 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1485421234

Digital Object Identifier
doi:10.1214/17-ECP46

Subjects
Primary: 60E05: Distributions: general theory 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
$G$-expectation nonlinear expectation distribution independence tightness

Rights
Creative Commons Attribution 4.0 International License.

Citation

Gao, Qiang; Hu, Mingshang; Ji, Xiaojun; Liu, Guomin. Product space for two processes with independent increments under nonlinear expectations. Electron. Commun. Probab. 22 (2017), paper no. 11, 12 pp. doi:10.1214/17-ECP46. https://projecteuclid.org/euclid.ecp/1485421234.


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References

  • [1] Denis, Laurent; Hu, Mingshang; Peng, Shige. Function spaces and capacity related to a sublinear expectation: application to $G$-Brownian motion paths. Potential Anal 34 (2011), no. 2, 139–161.
  • [2] Hu, Mingshang; Li, Xiaojuan. Independence under the $G$-expectation framework. J. Theoret. Probab 27 (2014), no. 3, 1011–1020.
  • [3] Hu, Ming-shang; Peng, Shi-ge. On representation theorem of $G$-expectations and paths of $G$-Brownian motion. Acta Math. Appl. Sin. Engl. Ser 25 (2009), no. 3, 539–546.
  • [4] Peng, Shige. Filtration consistent nonlinear expectations and evaluations of contingent claims. Acta Math. Appl. Sin. Engl. Ser 20 (2004), no. 2, 191–214.
  • [5] Peng, Shige. Nonlinear expectations and nonlinear Markov chains. Chinese Ann. Math. Ser. B 26 (2005), no. 2, 159–184.
  • [6] Peng, Shige. $G$-expectation, $G$-Brownian motion and related stochastic calculus of Itô type. Stochastic analysis and applications, 541–567, Abel Symp., 2, Springer, Berlin, 2007.
  • [7] Peng, Shige. Multi-dimensional $G$-Brownian motion and related stochastic calculus under $G$-expectation. Stochastic Process. Appl 118 (2008), no. 12, 2223–2253.
  • [8] Peng, Shige. A new central limit theorem under sublinear expectations, arXiv:0803.2656
  • [9] Peng, Shige. Nonlinear expectations and stochastic calculus under uncertainty, arXiv:1002.4546
  • [10] Peng, Shige. Tightness, weak compactness of nonlinear expectations and application to CLT, arXiv:1006.2541
  • [11] Song, Yongsheng. Characterizations of processes with stationary and independent increments under $G$-expectation. Ann. Inst. Henri Poincaré Probab. Stat 49 (2013), no. 1, 252–269.