RESEARCH ARTICLE

Multiple G-Itô integral in G-expectation space

  • Panyu WU
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  • Qilu Securities Institute for Financial Studies, Shandong University, Jinan 250100, China

Received date: 19 Nov 2010

Accepted date: 06 Jan 2013

Published date: 01 Apr 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

In 2007, Peng introduced Itô integral with respect to G-Brownian motion and the related Itô’s formula in G-expectation space. Motivated by the properties of multiple Wiener integral obtained by Itô in 1951, we introduce multiple G-Itô integral in G-expectation space, and investigate how to calculate it. Furthermore, We establish a relationship between Hermite polynomials and multiple G-Itô integrals.

Cite this article

Panyu WU . Multiple G-Itô integral in G-expectation space[J]. Frontiers of Mathematics in China, 2013 , 8(2) : 465 -476 . DOI: 10.1007/s11464-013-0288-8

1
Cheridito P, Soner H M, Touzi N. The multi-dimensional superreplication problem under gamma constraints. Ann Inst H Poincaré Anal Non Linéaire, 2005, 22(5): 633-666

DOI

2
Denis L, Hu M, Peng S. Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths. Potential Anal, 2011, 34: 139-161

DOI

3
Engel D D. The Multiple Stochastic Integral. Providence: Amer Math Soc, 1982

4
Hu M, Peng S. On representation theorem of G-expectations and paths of G-Brownian motion. Acta Math Appl Sin Engl Ser, 2009, 25(3): 539-546

DOI

5
It�o K. Multiple Wiener integral. J Math Soc Japan, 1951, 3: 157-164

DOI

6
Li X, Peng S. Stopping times and related Itô calculus with G-Brownian motion. Stochastic Process Appl, 2011, 121: 1492-1508

DOI

7
Peng S. G-expectation, G-Brownian motion and related stochastic calculus of Itô type. In: Stochastic Analysis and Applications, Abel Symposia. Berlin: Springer, 2007, 541-567

DOI

8
Peng S. G-Brownian motion and dynamic risk measure under volatility uncertainty. arXiv: 0711.2834v1 [math.PR]

9
Peng S. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation. Stochastic Process Appl, 2008, 118: 2223-2253

DOI

10
Peng S. Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations. Sci China Ser A, 2009, 52: 1391-1411

DOI

11
Peng S. Nonlinear expectations and stochastic calculus under uncertainty-with robust central limit theorem and G-Brownian motion. arXiv: 1002.4546v1 [math.PR]

12
Soner H M, Touzi N. Stochastic target problems, dynamic programming, and viscosity solutions. SIAM J Control Optim, 2002, 41(2): 404-424

DOI

13
Soner H M, Touzi N, Zhang J. Martingale representation theorem for the G-expectation. Stochastic Process Appl, 2011, 121(2): 265-287

DOI

14
Wiener N. The homogeneous chaos. Amer J Math, 1938, 60: 897-936

DOI

15
Xu J, Shang H, Zhang B. A Girsanov type theorem under G-framework. Stoch Anal Appl, 2011, 29: 386-406

DOI

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