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Mixed Stochastic Differential Equations: Existence and Uniqueness Result

José Luís da Silva · Mohamed Erraoui · El Hassan Essaky

27 citations0/0 files storedRePEc: Research Papers in Economics

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

Abstract

Abstract In this paper we establish an existence and uniqueness result for solutions of multidimensional, time-dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter $$H>1/2$$ H > 1 / 2 and a multidimensional standard Brownian motion under a weaker condition than the Lipschitz one.

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References

1968Fractional Brownian Motions, Fractional Noises and Applications 1998Differential equations driven by rough signals 1999Stochastic Analysis of the Fractional Brownian Motion 1998Integration with respect to fractal functions and stochastic calculus. I 2001Stochastic Calculus with Respect to Gaussian Processes 2002Differential equations driven by fractional Brownian motion 1996Existence of strong solutions for Itô's stochastic equations via approximations 2003Stochastic integration with respect to fractional brownian motion

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