Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Generators

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions

In this note, we study one-dimensional reflected backward stochastic differential equations (RBSDEs) driven by Countable Brownian Motions with one continuous barrier and continuous generators. Via a comparison theorem, we provide the existence of minimal and maximal solutions to this kind of equations.

existence and measurability of the solution of the stochastic differential equations driven by fractional brownian motion

Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion

We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter H ∈ (0, 1). A general framework is constructed to make precise the notions of “invariant measure” and “stationary state” for such a system. We then prove under rather weak dissipativity conditions that such an SDE possesses a unique st...

Stochastic differential equations driven by G-Brownian motion with reflecting boundary conditions

In this paper, we introduce the idea of stochastic integrals with respect to an increasing process in the G-framework and extend G-Itô’s formula. Moreover, we study the solvability of the scalar valued stochastic differential equations driven by G-Brownian motion with reflecting boundary conditions (RGSDEs).