Multiple G-Stratonovich Integral Driven by G-Brownian Motion

p-Moment stability of solutions to stochastic differential equations driven by G-Brownian motion

Stability theorem for stochastic differential equations driven by G-Brownian motion

In this paper, stability theorems for stochastic differential equations and backward stochastic differential equations driven by G-Brownian motion are obtained. We show the existence and uniqueness of solutions to forward-backward stochastic differential equations driven by G-Brownian motion. Stability theorem for forward-backward stochastic differential equations driven by G-Brownian motion is...

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).

Explicit solutions of G-heat equation with a class of initial conditions by G-Brownian motion

We obtain the viscosity solution of G-heat equation with the initial condition φ(x) = x for each integer n ≥ 1 using the method of G-Brownian motion.

The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6

Let B be a fractional Brownian motion with Hurst parameter H = 1/6. It is known that the symmetric Stratonovich-style Riemann sums for ∫ g(B(s)) dB(s) do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of càdlàg functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correcti...