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

Yiqing Lin (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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 $G$-Itô'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.

Mots clés: G-Brownian motion; G-expectation; Increasing Processes; G-Itô's formula; G-stochastic differential equations; Reflecting Boundary Conditions

Domaines: Probabilités [math.PR]

Yiqing Lin. Stochastic Differential Equations Driven by $G$-Brownian Motion with Reflecting Boundary Conditions. Electronic Journal of Probability, 2013, 18 (9), pp.1-23. ⟨10.1214/EJP.v18-2566⟩. ⟨hal-00704006⟩