In this paper, we first use PDE techniques and probabilistic methods to identify a kind of quasi-continuous random variables. Then we give a characterization of the G-integrable processes and get a kind of quasicontinuous processes by Krylov's estimates. This result is useful for the development of G-stochastic analysis theory. Moreover, it also provides a tool for the study of the non-Markovian Itô processes.
The present paper considers a new kind of backward stochastic differential equations (BSDEs) driven by G-Brownian motion, which is called ergodic G-BSDEs. Firstly, the well-posedness of G-BSDEs with infinite horizon is given by a new linearization method. Then, the Feynman-Kac formula for fully nonlinear elliptic partial differential equations (PDEs) is established. Moreover, a new probabilistic approach is introduced to prove the uniqueness of viscosity solution to elliptic PDEs in the whole space. Finally, we obtain the existence of solution to G-EBSDE and some applications are also stated.
The present paper is devoted to the study of the well-posedness of BS-DEs with mean reflection whenever the generator has quadratic growth in the z argument. This work is the sequel of [6] in which a notion of BSDEs with mean reflection is developed to tackle the super-hedging problem under running risk management constraints. By the contraction mapping argument, we first prove that the quadratic BSDE with mean reflection admits a unique deterministic flat local solution on a small time interval whenever the terminal value is bounded. Moreover, we build the global solution on the whole time interval by stitching local solutions when the generator is uniformly bounded with respect to the y argument.
In this paper we study the problems of invariant and ergodic measures under G-expectation framework. In particular, the stochastic differential equations driven by G-Brownian motion (G-SDEs) have the unique invariant and ergodic measures. Moreover, the invariant and ergodic measures of G-SDEs are also sublinear expectations. However, the invariant measures may not coincide with ergodic measures, which is different from the classical case.
In this paper, we show that the integration of a stochastic differential equation driven by G-Brownian motion (G-SDE for short) in R can be reduced to the integration of an ordinary differential equation (ODE for short) parametrized by a variable in (Ω, F). By this result, we obtain a comparison theorem for G-SDEs and its applications.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.