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Representation Formulae for the Fractional Brownian Motion
14 references·8 citing·39 second hop
Representation Formulae for the Fractional Brownian Motion (2010)Representation Formulae for the Fractiona…Transformation formulas for fractional Brownian motion (2006)Transformation formulas for f…Spherical and Hyperbolic Fractional Brownian Motion (2005)Spherical and Hyperbolic Frac…A series expansion of fractional Brownian motion (2004)A series expansion of fractio…Fractional Ornstein-Uhlenbeck processes (2003)Fractional Ornstein-Uhlenbeck…Equivalence of Volterra processes (2003)Equivalence of Volterra proce…Stochastic analysis, rough path analysis and fractional Brownian motions (2002)Stochastic analysis, rough pa…Mixed Fractional Brownian Motion (2001)Mixed Fractional Brownian Mot…Are Classes of Deterministic Integrands for Fractional Brownian Motion on an Interval Complete? (2001)Are Classes of Deterministic …Stochastic Analysis of the Fractional Brownian Motion (1999)Stochastic Analysis of the Fr…On Fractional Brownian Processes (1999)On Fractional Brownian Proces…An Elementary Approach to a Girsanov Formula and Other Analytical Results on Fractional Brownian Motions (1999)An Elementary Approach to a G…Alternative forms of fractional Brownian motion (1999)Alternative forms of fraction…On the prediction of fractional Brownian motion (1996)On the prediction of fraction…Fractional Brownian Motions, Fractional Noises and Applications (1968)Fractional Brownian Motions, …Functional central limit theorems for rough volatility (2024)Functional central limit theo…Deep Curve-Dependent PDEs for Affine Rough Volatility (2023)Deep Curve-Dependent PDEs for…Distribution dependent SDEs driven by additive fractional Brownian motion (2022)Distribution dependent SDEs d…Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness (2021)Time-inhomogeneous Gaussian s…Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model (2020)Hierarchical adaptive sparse …Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions (2019)Gaussian stochastic volatilit…Some sample path properties of multifractional Brownian motion (2015)Some sample path properties o…White noise-based stochastic calculus with respect to multifractional Brownian motion (2013)White noise-based stochastic …Stochastic Differential Equations and Diffusion Processes (1983)Continuous Martingales and Brownian Motion (1999)Differential equations driven by fractional Brownian motion (2002)Brownian Motion and Stochastic Calculus (2007)Differential Equations Driven by Rough Paths (2007)Multidimensional Stochastic Processes as Rough Paths (2010)Integration questions related to fractional Brownian motion (2000)Stochastic Calculus for Fractional Brownian Motion I. Theory (2000)Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H∈(0,12) (2005)A decomposition of the bifractional Brownian motion and some applications (2008)Weak convergence to fractional brownian motion and to the rosenblatt process (1975)Multiple Time Series Regression with Integrated Processes (1986)Semiparametric fractional cointegration analysis (2001)Nonstationarity-extended local Whittle estimation (2007)EXACT LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION WITH UNKNOWN MEAN AND TIME TREND (2009)The Pricing of Options and Corporate Liabilities (1973)Arbitrage in fractional Brownian motion models (2003)On bifractional Brownian motion (2005)Stochastic Integration and Differential Equations (2005)Some properties of the sub-fractional Brownian motion (2006)Stochastic Integration and Differential Equations (1990)Log-Periodogram Regression of Time Series with Long Range Dependence (1995)Pricing under rough volatility (2015)Volatility Is Rough (2018)Calcul d'ito sans probabilites (1981)Dirichlet Forms and Analysis on Wiener Space (1991)Stochastic Calculus with Respect to Gaussian Processes (2001)FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE (2003)Independence and Dependence (1961)The Typical Spectral Shape of an Economic Variable (1966)AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING (1980)THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS (1983)Empirical properties of asset returns: stylized facts and statistical issues (2001)The Typical Spectral Shape of an Economic Variable (2001)Limit Theorems for Stochastic Processes (2003)Long Range Dependence (2004)A storage model with self-similar input (1994)On the Wiener integral with respect to a sub-fractional Brownian motion on an interval (2008)The stochastic wave equation with fractional noise: A random field approach (2010)
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References

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  • 1999Stochastic Analysis of the Fractional Brownian Motion744 cited
  • 2003Fractional Ornstein-Uhlenbeck processes418 cited
  • 1999An Elementary Approach to a Girsanov Formula and Other Analytical Results on Fractional Brownian Motions401 cited
  • 2001Mixed Fractional Brownian Motion389 cited
  • 2002Stochastic analysis, rough path analysis and fractional Brownian motions317 cited
  • 1999Alternative forms of fractional Brownian motion289 cited
  • 1996On the prediction of fractional Brownian motion205 cited
  • 2004A series expansion of fractional Brownian motion159 cited
  • 2001Are Classes of Deterministic Integrands for Fractional Brownian Motion on an Interval Complete?134 cited
  • 1999On Fractional Brownian Processes98 cited
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  • 2003Equivalence of Volterra processes65 cited
  • 2005Spherical and Hyperbolic Fractional Brownian Motion59 cited

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  • 2024Functional central limit theorems for rough volatility46 cited

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2023
Deep Curve-Dependent PDEs for Affine Rough Volatility
33 cited
  • 2022Distribution dependent SDEs driven by additive fractional Brownian motion32 cited
  • 2013White noise-based stochastic calculus with respect to multifractional Brownian motion22 cited
  • 2020Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model17 cited
  • 2019Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions16 cited
  • 2015Some sample path properties of multifractional Brownian motion16 cited
  • 2021Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness15 cited