Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion
By João Guerra, David Nualart. 2008
152 citations recorded by the source corpus.
Abstract 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 classical Itô stochastic calculus. The existence result is based on the Yamada–Watanabe theorem.
Subfields: Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f31315e10ac027258e507fbbbad34a042009e85b
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In Mathematical Physics
Citations in the corpus
- Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst Index H > 1/2 (2011, unknown): “Unique solvability or (1) was proved in [8] for time-independent coefficients and zero drift, [10] forH ∈ (3/4, 1) and bounded coefficients, and in [5] for anyH > 1/2, but under the assumption that W and B are independent.”
- Averaging principle for fast-slow system driven by mixed fractional Brownian rough path (2020, background): “To establish the averaging principle (see Theorem 1.2), we combine the rough path analysis and the pathwise approach via fractional calculus inspired by the work of Hu and Nualart [15].”
- On drift parameter estimation in models with fractional Brownian motion (2011, background): “Remark 1 In case when components W and BH are independent, assumptions for the coefficients can be relaxed, as it has been shown in [17].”