Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes

DOI10.1016/j.spa.2018.08.002zbMath1422.60091arXiv1612.00498OpenAlexW2560048775MaRDI QIDQ2274279

Lasse Leskelä, Lauri Viitasaari, Zhe Chen

Publication date: 19 September 2019

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.00498

zbMATH Keywords

fractional calculusbounded \(p\)-variationfractional Sobolev spaceRiemann-Liouville integralcomposite stochastic processfractional Sobolev-Slobodeckij spaceGagliardo-Slobodeckij seminormgeneralised Stieltjes integral

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) Fractional derivatives and integrals (26A33) General theory of stochastic processes (60G07) Stochastic integrals (60H05)

Related Items (5)

Sobolev regularity of occupation measures and paths, variability and compositions ⋮ Stochastic differential equations with discontinuous diffusion coefficients ⋮ Forward integration of bounded variation coefficients with respect to Hölder continuous processes ⋮ Variability of paths and differential equations with \(\mathrm{BV}\)-coefficients ⋮ On sharp rate of convergence for discretization of integrals driven by fractional Brownian motions and related processes with discontinuous integrands

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On probability laws of solutions to differential systems driven by a fractional Brownian motion
• Processes iterated ad libitum
• Properties and numerical evaluation of the Rosenblatt distribution
• Hitchhiker's guide to the fractional Sobolev spaces
• Necessary and sufficient conditions for Hölder continuity of Gaussian processes
• Fractional processes and fractional-order signal processing. Techniques and applications
• Probability tails of Gaussian extrema
• On irregular functionals of SDEs and the Euler scheme
• Fractional-order systems and controls. Fundamentals and applications
• Integration with respect to fractal functions and stochastic calculus. I
• Differential equations driven by rough signals
• On weak Brownian motions of arbitrary order
• Differential equations driven by fractional Brownian motion
• Fractional {O}rnstein-{U}hlenbeck processes
• Iterating Brownian motions, ad libitum
• Rate of convergence for discretization of integrals with respect to fractional Brownian motion
• How rich is the class of multifractional Brownian motions?
• Introduction to stochastic calculus for finance. A new didactic approach.
• Integration with respect to Fractal Functions and Stochastic Calculus II
• Integral representations of some functionals of fractional Brownian motion
• ESTIMATES FOR THE SOLUTION TO STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER H ∈ (⅓, ½)
• On hedging European options in geometric fractional Brownian motion market model
• Fractional Splines and Wavelets
• Wiener Integrals with Respect to the Hermite Process and a Non-Central Limit Theorem
• Stochastic finance. An introduction in discrete time
• A course on rough paths. With an introduction to regularity structures

This page was built for publication: Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes