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

• Published in: Communications in statistics. Theory and methods Vol. 40; no. 19-20; pp. 3492 - 3508
• Main Authors: Mishura, Yulia S., Shevchenko, Georgiy M.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01-10-2011; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Euler approximation; Exact sciences and technology; Fractional Brownian motion; General topics; Mathematics; Mixed stochastic differential equation; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Pathwise integral; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Stochastic analysis; Solution uniqueness; 60J65; Pathwise integral; 60G22; 60H10; Approximation; Differential equation; Existence of solution; Fractional brownian motion; Wiener process; Fractional process; Mixed equation; Brownian motion; Statistical method; Euler approximation; Integral; Integral equation; Mixed stochastic differential equation; 60G15; Stochastic equation
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2011.581174

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.