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Generalized iterated-sums signatures
Joscha Diehl, Kurusch Ebrahimi-Fard, Nikolas Tapia
We explore the algebraic properties of a generalized version of the iterated-sums signature, inspired by previous work of F.~Király and H.~Oberhauser. In particular, we show how to…
Tropical time series, iterated-sums signatures and quasisymmetric functions
Joscha Diehl, Kurusch Ebrahimi-Fard, Nikolas Tapia
Aiming for a systematic feature-extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of the tropical semiring is a c…
Generating Series for Networks of Chen-Fliess Series
W. Steven Gray, Kurusch Ebrahimi-Fard
Consider a set of single-input, single-output nonlinear systems whose input-output maps are described only in terms of convergent Chen-Fliess series without any assumption that fin…
Bogoliubov type recursions for renormalisation in regularity structures
Yvain Bruned, Kurusch Ebrahimi-Fard
Hairer's regularity structures transformed the solution theory of singular stochastic partial differential equations. The notions of positive and negative renormalisation are centr…
Cumulant-cumulant relations in free probability theory from Magnus' expansion
A. Celestino, K. Ebrahimi-Fard, F. Patras +1
Relations between moments and cumulants play a central role in both classical and non-commutative probability theory. The latter allows for several distinct families of cumulants c…
Quasi-shuffle algebras in non-commutative stochastic calculus
Kurusch Ebrahimi-Fard, Frédéric Patras
This chapter is divided into two parts. The first is largely expository and builds on Karandikar's axiomatisation of It{ô} calculus for matrix-valued semimartin-gales. Its aim is t…
Wick polynomials in non-commutative probability
K. Ebrahimi-Fard, F. Patras, N. Tapia +1
Wick polynomials and Wick products are studied in the context of non-commutative probability theory. It is shown that free, boolean and conditionally free Wick polynomials can be d…