Lévy processes and quasi-shuffle algebras

DOI10.1080/17442508.2013.865131zbMath1337.60152arXiv1311.1683OpenAlexW2061366630MaRDI QIDQ2812015

Kurusch Ebrahimi-Fard, Charles Curry, Anke Wiese, Simon J. A. Malham

Publication date: 10 June 2016

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.1683

zbMATH Keywords

Lévy processessemimartingalesTeugels martingalesquasi-shuffle algebra

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Applications of stochastic analysis (to PDEs, etc.) (60H30) Martingales with continuous parameter (60G44)

Related Items (7)

Flows and stochastic Taylor series in Itô calculus ⋮ Smooth rough paths, their geometry and algebraic renormalization ⋮ Quasi‐shuffle algebras and renormalisation of rough differential equations ⋮ Quasi-geometric rough paths and rough change of variable formula ⋮ An isomorphism between branched and geometric rough paths ⋮ Algebraic structures and stochastic differential equations driven by Lévy processes ⋮ Quasi-shuffle algebras in non-commutative stochastic calculus

Cites Work

• Unnamed Item
• Quasi-shuffle products revisited
• The multiplicity of an increasing family of \(\sigma\)-fields
• Chaotic and predictable representations for Lévy processes.
• Quasi-shuffle products
• Mixable shuffles, quasi-shuffles and Hopf algebras.
• Modeling and approximation of stochastic differential equations driven by semimartingales^†
• Algebraic structure of multiple stochastic integrals with respect to brownian motions and poisson processes
• The algebra of iterated stochastic integrals
• Stochastic expansions and Hopf algebras
• Algebraic structure of stochastic expansions and efficient simulation

This page was built for publication: Lévy processes and quasi-shuffle algebras