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Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst IndexH > 1/2

Yuliya Stepanovna Mishura · Georgiy M. Shevchenko

60 citations0/0 files storedCommunication in Statistics- Theory and Methods

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Fuzzy Systems and Optimization

Abstract

We consider a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficients, it is proved that the equation has a unique solution.

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References

2008Stochastic Calculus for Fractional Brownian Motion and Related Processes 1998Integration with respect to fractal functions and stochastic calculus. I 2002Differential equations driven by fractional Brownian motion 2002Stochastic analysis, rough path analysis and fractional Brownian motions 2008Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation 2008Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion 2007Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion 2008The rate of convergence for Euler approximations of solutions of stochastic differential equations driven by fractional Brownian motion

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2014On drift parameter estimation in models with fractional Brownian motion 2013Mixed fractional stochastic differential equations with jumps 2015Mixed stochastic delay differential equations

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