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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
10 references·3 citing·38 second hop
Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst IndexH > 1/2 (2011)Existence and Uniqueness of the Solution …The rate of convergence for Euler approximations of solutions of stochastic differential equations driven by fractional Brownian motion (2008)The rate of convergence for E…Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion (2008)Stochastic Differential Equat…Stochastic Calculus for Fractional Brownian Motion and Related Processes (2008)Stochastic Calculus for Fract…Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation (2008)Differential Equations Driven…Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion (2007)Exact Rate of Convergence of …The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type (2002)The existence and uniqueness …Stochastic analysis, rough path analysis and fractional Brownian motions (2002)Stochastic analysis, rough pa…Differential equations driven by fractional Brownian motion (2002)Differential equations driven…Integration with respect to fractal functions and stochastic calculus. I (1998)Integration with respect to f…Fractional Brownian motion: theory and applications (1998)Fractional Brownian motion: t…Mixed stochastic delay differential equations (2015)Mixed stochastic delay differ…On drift parameter estimation in models with fractional Brownian motion (2014)On drift parameter estimation…Mixed fractional stochastic differential equations with jumps (2013)Mixed fractional stochastic d…Fractional Brownian Motions, Fractional Noises and Applications (1968)Differential equations driven by rough signals (1998)Stochastic Analysis of the Fractional Brownian Motion (1999)Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion (2008)Fractional stochastic differential equations with applications to finance (2012)FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE (2003)Controlled differential equations as Young integrals: A simple approach (2010)A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion (2012)0 A MILSTEIN-TYPE SCHEME WITHOUT LEVY AREA TERMS FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION (2013)Numerical solution of stochastic differential equations (2016)Stochastic Differential Equations and Diffusion Processes (1983)Continuous Martingales and Brownian Motion (1999)Stochastic integration with respect to fractional brownian motion (2003)Brownian Motion and Stochastic Calculus (2007)Differential Equations Driven by Rough Paths (2007)Multiple Wiener Integral (1951)Integration questions related to fractional Brownian motion (2000)Stochastic Calculus with Respect to Gaussian Processes (2001)Stochastic Flows and Stochastic Differential Equations (1998)Continuous-time trading and the emergence of probability (2012)Integrability and tail estimates for Gaussian rough differential equations (2013)Geometric versus non-geometric rough paths (2015)The Malliavin Calculus and Related Topics (1995)The Malliavin Calculus and Related Topics (2006)Parameter estimation for the discretely observed fractional Ornstein–Uhlenbeck process and the Yuima R package (2012)Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions (2016)On the uniqueness of solutions of stochastic differential equations (1971)Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion (2019)Averaging dynamics driven by fractional Brownian motion (2020)Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion (2022)La variation d'ordre p des semi-martingales (1976)Stochastic analysis of fractional brownian motions (1995)Mixed stochastic differential equations with long-range dependence: Existence, uniqueness and convergence of solutions (2012)ESTIMATORS FOR LONG-RANGE DEPENDENCE: AN EMPIRICAL STUDY (1995)Log-Periodogram Regression of Time Series with Long Range Dependence (1995)Stochastic averaging principle for dynamical systems with fractional Brownian motion (2014)Hurst Exponent Analysis: Evidence from Volatility Indices and the Volatility of Volatility Indices (2023)Hybrid scheme for Brownian semistationary processes (2017)
this work references cited by second hop

References

  • 2008Stochastic Calculus for Fractional Brownian Motion and Related Processes922 cited
  • 1998Integration with respect to fractal functions and stochastic calculus. I589 cited
  • 2002Differential equations driven by fractional Brownian motion408 cited
  • 2002Stochastic analysis, rough path analysis and fractional Brownian motions317 cited
  • 2008Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation156 cited
  • 2008Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion143 cited
  • 2007Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion100 cited
  • 2008The rate of convergence for Euler approximations of solutions of stochastic differential equations driven by fractional Brownian motion81 cited
  • 1998Fractional Brownian motion: theory and applications73 cited
  • 2002The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type65 cited

Cited by

  • 2014On drift parameter estimation in models with fractional Brownian motion51 cited
  • 2013Mixed fractional stochastic differential equations with jumps40 cited
  • 2015Mixed stochastic delay differential equations29 cited

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