Stochastic sub-diffusion equation with conformable derivative driven by standard Brownian motion

A singular stochastic differential equation driven by fractional Brownian motion∗

In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter H > 1 2 . Under some assumptions on the drift, we show that there is a unique solution, which has moments of all orders. We also apply the techniques of Malliavin calculus to prove that the solution has an absolutely continuous law at any time t > 0.

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the c...

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

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

On Delayed Logistic Equation Driven by Fractional Brownian Motion

In this paper we use the fractional stochastic integral given by Carmona et al. [1] to study a delayed logistic equation driven by fractional Brownian motion which is a generalization of the classical delayed logistic equation . We introduce an approximate method to find the explicit expression for the solution. Our proposed method can also be applied to the other models and to illustrate this,...