On stochastic integration for volatility modulated Brownian-driven Volterra processes via white noise analysis

DOI10.1142/S0219025714500118zbMath1291.60109arXiv1303.4625OpenAlexW1974495175MaRDI QIDQ5170127

Benedykt Szozda, Fred Espen Benth, Ole Eiler Barndorff-Nielsen

Publication date: 18 July 2014

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.4625

zbMATH Keywords

white noise analysisstochastic integralMalliavin derivativeSkorohod integralVolterra processvolatility modulation

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) White noise theory (60H40) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items

Ambit Fields: Survey and New Challenges ⋮ Stochastic integrals and Gelfand integration in Fréchet spaces ⋮ On stochastic integration for volatility modulated Lévy-driven Volterra processes ⋮ Selfdecomposable fields ⋮ Some Recent Developments in Ambit Stochastics ⋮ A Weak Limit Theorem for Numerical Approximation of Brownian Semi-stationary Processes ⋮ A Donsker delta functional approach to optimal insider control and applications to finance ⋮ Dynamical properties of endomorphisms, multiresolutions, similarity and orthogonality relations ⋮ Gamma Kernels and BSS/LSS Processes ⋮ A generalised Itō formula for Lévy-driven Volterra processes

Cites Work

• Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes
• Stochastic partial differential equations. A modeling, white noise functional approach
• Stochastic integration with respect to Gaussian processes.
• Stochastic integration with respect to Volterra processes
• On a dual pair of spaces of smooth and generalized random variables
• On stochastic integration for volatility modulated Lévy-driven Volterra processes
• ON WEIGHTEDL²(Ω)-SPACES, THEIR DUALS AND ITÔ INTEGRATION
• On the martingale property for generalized stochastic processes
• The Malliavin Calculus and Related Topics
• THE GROSS DERIVATIVE AND GENERALIZED RANDOM VARIABLES
• White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance
• Using the Donsker delta function to compute hedging strategies