Quasi-shuffle algebras in non-commutative stochastic calculus - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2021

Quasi-shuffle algebras in non-commutative stochastic calculus

Résumé

This chapter is divided into two parts. The first is largely expository and builds on Karandikar's axiomatisation of Itô calculus for matrix-valued semimartin-gales. Its aim is to unfold in detail the algebraic structures implied for iterated Itô and Stratonovich integrals. These constructions generalise the classical rules of Chen calculus for deterministic scalar-valued iterated integrals. The second part develops the stochastic analog of what is commonly called chronological calculus in control theory. We obtain in particular a pre-Lie Magnus formula for the logarithm of the Itô stochastic exponential of matrix-valued semimartingales.
Fichier principal
Vignette du fichier
EFP_Karandikar.pdf (200.58 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02541173 , version 1 (13-04-2020)

Identifiants

Citer

Kurusch Ebrahimi-Fard, Frédéric Patras. Quasi-shuffle algebras in non-commutative stochastic calculus. International Conference on Random Transformations and Invariance in Stochastic Dynamics, Stefania Ugolini, Marco Fuhrman, Elisa Mastrogiacomo, Paola Morando, Barbara Rüdiger, 2019, Verona, Italy. pp.89-112. ⟨hal-02541173⟩
59 Consultations
159 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More