Stochastic Differential Equations Driven by $G$-Brownian Motion with Reflecting Boundary Conditions

Details Stochastic Differential Equations Driven by $G$-Brownian Motion with Reflecting Boundary Conditions Stochastic Differential Equations Driven by $G$-Brownian Motion with Reflecting Boundary Conditions

2011-03-02

arxiv.org/abs/1103.0392v3

Mathematics

Probability

Scientific paper

In this paper, we introduce the idea of integral with respect to increasing processes under the framework of $G$-expectation and give the proof of extended $G$-It\^o's formula. Moreover, we study the existence and uniqueness of solutions to the scalar valued stochastic differential equations driven by $G$-Brownian motion with reflecting boundary conditions (RGSDEs), and give a comparison theorem.

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