Quasi-shuffle algebras in non-commutative stochastic calculus

Understand

This chapter is divided into two parts.

• The first is largely expository and builds on Karandikar's axiomatisation of It{\^o} calculus for matrix-valued semimartin-gales.
• Its aim is to unfold in detail the algebraic structures implied for iterated It{\^o} and Stratonovich integrals.
• These constructions generalise the classical rules of Chen calculus for deterministic scalar-valued iterated integrals.