Function spaces and capacity related to a Sublinear Expectation: application to G-Brownian Motion Pathes

Abstract

In this paper we give some basic and important properties of several typical Banach spaces of functions of $G$-Brownian motion pathes induced by a sublinear expectation--G-expectation. Many results can be also applied to more general situations. A generalized version of Kolmogorov's criterion for continuous modification of a stochastic process is also obtained. The results can be applied to continuous time dynamic and coherent risk measures in finance in particular for path-dependence risky positions under situations of volatility model uncertainty.

26 pages

Cited by in corpus (25)

• Martingale Representation Theorem for the G-expectation
• Some properties on $G$-evaluation and its applications to $G$-martingale decomposition
• A New Central Limit Theorem under Sublinear Expectations
• Dual formulation of second order target problems
• Donsker's invariance principle under the sub-linear expectation with an application to Chung's law of the iterated logarithm
• A law of the iterated logarithm sublinear expectations
• Note on Viscosity Solution of Path-Dependent PDE and G-Martingales
• G-Lévy Processes under Sublinear Expectations
• Tightness, weak compactness of nonlinear expectations and application to CLT
• Local time and Tanaka formula for G-Brownian Motion
• Self-normalized moderate deviation and laws of the iterated logarithm under G-expectation
• Dynamic risk measuring under model uncertainty: taking advantage of the hidden probability measure
• On exponential stability for stochastic differential equations disturbed by G-Brownian motion
• Properties of hitting times for $G$-martingale
• Supermartingale Decomposition Theorem under G-expectation
• Path Independence of Additive Functionals for SDEs under G-framework
• Stopping Times and Related Itô's Calculus with G-Brownian Motion
• Wellposedness of Second Order Backward SDEs
• G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion in Quantum Mechanics
• On the Representation Theorem of G-Expectations and Paths of G--Brownian Motion
• The Independence under Sublinear Expectations
• Backward stochastic differential equations under super linear G-expectation and associated Hamilton-Jacobi-Bellman equations
• On representation theorem of sublinear expectation related to G-Lévy process and paths of G-Lévy process
• Characterizations of processes with stationary and independent increments under $G$-expectation
• Functional central limit theorems for random vectors under sub-linear expectations