Infinite dimensional pathwise Volterra processes driven by Gaussian noise -- probabilistic properties and applications --
From MaRDI portal
Publication:2243926
DOI10.1214/21-EJP683zbMath1491.60073arXiv2005.14460OpenAlexW3197623917MaRDI QIDQ2243926
Fabian A. Harang, Fred Espen Benth
Publication date: 11 November 2021
Published in: Electronic Journal of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.14460
Hilbert spaceGaussian processesfractional differential equationsVolterra integral equationscovariance operatorrough volatility modelsrough path integrationinfinite dimensional stochastic analysis
Stochastic integrals (60H05) Volterra integral equations (45D05) Stochastic integral equations (60H20)
Related Items
Volterra equations driven by rough signals 2: Higher-order expansions ⋮ Volterra equations driven by rough signals. III: Probabilistic construction of the Volterra rough path for fractional Brownian motions ⋮ A weak law of large numbers for realised covariation in a Hilbert space setting
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Representation of infinite-dimensional forward price models in commodity markets
- Stochastic partial differential equations: an introduction
- Iterated stochastic processes: simulation and relationship with high order partial differential equations
- A construction of the rough path above fractional Brownian motion using Volterra's representation
- A generalized Gronwall inequality and its application to a fractional differential equation
- Differential equations driven by rough paths. Ecole d'Eté de Probabilités de Saint-Flour XXXIV -- 2004. Lectures given at the 34th probability summer school, July 6--24, 2004.
- Hölder-continuous rough paths by Fourier normal ordering
- Fractional diffusion equations and processes with randomly varying time
- Stochastic and multiple Wiener integrals for Gaussian processes
- Brownian motion in a Brownian crack
- A parabolic stochastic differential equation with fractional Brownian motion input
- Stochastic evolution equations with fractional Brownian motion
- Ornstein-Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility
- A fractional epidemiological model for computer viruses pertaining to a new fractional derivative
- An extension of the sewing lemma to hyper-cubes and hyperbolic equations driven by multi-parameter Young fields
- FRACTIONAL BROWNIAN MOTION AND STOCHASTIC EQUATIONS IN HILBERT SPACES
- Derivatives Pricing in Energy Markets: An Infinite-Dimensional Approach
- Volatility is rough
- The Heston stochastic volatility model in Hilbert space
- Ambit Stochastics
- Young-Stieltjes integrals with respect to Volterra covariance functions
- Stochastic Partial Differential Equations with Levy Noise
- The characteristic function of rough Heston models
- A course on rough paths. With an introduction to regularity structures
- Stochastic Equations in Infinite Dimensions
