Martingale characterization of G-Brownian motion

By Jingqin Xu, Bo Zhang. 2009

85 citations recorded by the source corpus.

Abstract In this paper, we study the martingale characterization of G-Brownian motion, which was defined by Peng (cf. http://abelsymposium.no/symp2005/preprints/peng.pdf ) in 2006. As an application, we present a method for constructing a G-Brownian motion using a Markov chain. Furthermore, we obtain the representation theorem for some special symmetric martingales in the G-framework.

Subfields: Demography, Finance

View Paper: https://www.semanticscholar.org/paper/942d796105d6b9bd2304213b31f1a3f2ddfc5142

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Citations in the corpus

Martingale Representation Theorem for the G-Expectation (2010, background): “A partial answer to this question was already provided by Xu and Zhang [23] for the class of symmetric G-martingales, i.”
On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients (2010, background): “Based on the great efforts of many authors, such as Xu and Zhang[17], Soner et al.[13] and Song[14,15], Peng et al.[11] have given a complete theory for G-martingale representation.”
A complete representation theorem for G-martingales (2012, background): “The first partial answer was provided by Xu and Zhang [28]: if Y is a symmetric G-martingale, that is both Y and 2Y are G-martingales, then dYt ¼ Zt dBt for some process Z: ð1:4Þ However, symmetric G-martingales capture only the linear part in this nonlinear framework, and it is important to underst”
Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011, background): “For a more general X ∈ L2 G (ΩT ) with E[X] = −E[−X], Xu and Zhang (2009) proved the following representation: there exists a unique process Z ∈ M2 G (0, T ) such that Et[X] = E[X]+ ∫ t 0 ZsdBs, t ∈ [0, T ].”
Stochastic functional differential equations with infinite delay driven by G‐Brownian motion (2013, background): “Zhang D, Chen Z. Exponential stability for stochastic differential equation driven by G-Brownian motion.”
Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion (2009, methodology): “A martingale characterization of G-Brownian motion was given in [15].”