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.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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