Geometric Brownian motion

Statistics

Fractional Brownian motion

Brownian motion

Reflected Brownian motion

Mathematical analysis

Economics

Convergence (economics)

Applied mathematics

Innovation diffusion

Mathematics

Computer science

Economic growth

Stochastic differential equation

Brownian excursion

Knowledge management

Wiener process

Stochastic calculus

Diffusion process

Differential equation

Stochastic process

Stochastic partial differential equation

Applied Mathematics Letters

In this paper, an averaging principle for multidimensional, time dependent, stochastic differential equations (SDEs) driven by fractional Brownian motion and standard Brownian motion was established. We combined the pathwise approach with the Itô stochastic calculus to handle both types of integrals involved and proved that the original SDEs can be approximated by averaged SDEs in the manner of mean square convergence.

Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion