120 citations · 691 across the 56 of their papers we have counts for
13 papers · 1 filter
The Exponential Lie Series and a Chen-Strichartz Formula for Levy Processes
Kurusch Ebrahimi-Fard, Frederic Patras, Anke Wiese
In this paper, we derive a Chen-Strichartz formula for stochastic differential equations driven by Levy processes, that is, we derive a series expansion of the logarithm of the flo…
Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability
Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia +1
We study a particular group law on formal power series in non-commuting variables induced by their interpretation as linear forms on a suitable graded connected word Hopf algebra.…
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…
A group-theoretical approach to conditionally free cumulants
Kurusch Ebrahimi-Fard, Frederic Patras
In this work we extend the recently introduced group-theoretical approach to moment-cumulant relations in non-commutative probability theory to the notion of conditionally free cum…
Hopf-algebraic deformations of products and Wick polynomials
Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia +1
We present an approach to classical definitions and results on cumulant--moment relations and Wick polynomials based on extensive use of convolution products of linear functionals…
The exponential Lie series for continuous semimartingales
Kurusch Ebrahimi-Fard, Simon J. A. Malham, Frederic Patras +1
We consider stochastic differential systems driven by continuous semimartingales and governed by non-commuting vector fields. We prove that the logarithm of the flowmap is an expon…
Flows and stochastic Taylor series in Ito calculus
Kurusch Ebrahimi-Fard, Simon J. A. Malham, Frederic Patras +1
For stochastic systems driven by continuous semimartingales an explicit formula for the logarithm of the Ito flow map is given. A similar formula is also obtained for solutions of…
Convergence of U-statistics for interacting particle systems
P. Del Moral, F. Patras, S. Rubenthaler
The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assum…
Tree based functional expansions for Feynman--Kac particle models
Pierre Del Moral, Frédéric Patras, Sylvain Rubenthaler
We design exact polynomial expansions of a class of Feynman--Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related comb…
The convergence to equilibrium of neutral genetic models
Pierre Del Moral, Laurent Miclo, Frédéric Patras +1
This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree base…
Coalescent tree based functional representations for some Feynman-Kac particle models
Pierre Del Moral, Frédéric Patras, Sylvain Rubenthaler
We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting parti…