Browsing NTNU Open by Author "EbrahimiFard, Kurusch"
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Algebraic structures and stochastic differential equations driven by Levy processes
Curry, Charles Henry Alexander; EbrahimiFard, Kurusch; Malham, Simon J. A.; Wiese, Anke (Peer reviewed; Journal article, 2019)We construct an efficient integrator for stochastic differential systems driven by Lévy processes. An efficient integrator is a strong approximation that is more accurate than the corresponding stochastic Taylor approximation, ... 
Cumulants in Noncommutative:Probability via Hopf Algebras
Rodriguez, Adrian de Jesus Celestino (Doctoral theses at NTNU;2022:370, Doctoral thesis, 2022)The notion of cumulants plays a significant role in the combinatorial study of noncommutative probability theory. In this thesis, we study several problems associated with the notions of cumulants for free, Boolean and ... 
Cumulants, free cumulants and halfshuffles
EbrahimiFard, Kurusch; Patras, Frederic (Peer reviewed; Journal article, 2015)Free cumulants were introduced as the proper analogue of classical cumulants in the theory of free probability. There is a mix of similarities and differences, when one considers the two families of cumulants. Whereas the ... 
Decompositions of nonlinear input–output systems to zero the output
Gray, W. Steven; EbrahimiFard, Kurusch; Schmeding, Alexander (Journal article; Peer reviewed, 2024)Consider an input–output system where the output is the tracking error given some desired reference signal. It is natural to consider under what conditions the problem has an exact solution, that is, the tracking error is ... 
The Faá di Bruno Hopf algebra for multivariable feedback recursions in the center problem for higher order Abel equations
EbrahimiFard, Kurusch; Gray, W. Steven (Peer reviewed; Journal article, 2019)Poincaré’s center problem asks for conditions under which a planar polynomial system of ordinary differential equations has a center. It is well understood that the Abel equation naturally describes the problem in a ... 
Hopfalgebraic Deformations of Products and Wick Polynomials
EbrahimiFard, Kurusch; Patras, Frederic; Tapia, Nikolas; Zambotti, Lorenzo (Journal article; Peer reviewed, 2018)We present an approach to cumulant–moment relations and Wick polynomials based on extensive use of convolution products of linear functionals on a coalgebra. This allows, in particular, to understand the construction of ... 
Magnus Expansion in Gauge Theories
Fredheim, Håkon Richard (Master thesis, 2022)Noen uttrykk for løsningen på en ordinær differensiallikning utledes ved hjelp av en metode som innebærer Taylorrekkeutvikling av vektorfeltet som definerer differensiallikningen. En generalisering av et kjent resultat ... 
Monotone, free, and boolean cumulants: a shuffle algebra approach
EbrahimiFard, Kurusch; Patras, Frederic (Journal article; Peer reviewed, 2018)The theory of cumulants is revisited in the “Rota way”, that is, by following a combinatorial Hopf algebra approach. Monotone, free, and boolean cumulants are considered as infinitesimal characters over a particular ... 
Multiplicative and semimultiplicative functions on noncrossing partitions, and relations to cumulants
EbrahimiFard, Kurusch; Celestino, Adrián; Witzman, Leon; Perales, Daniel; Nica, Alexandru (Peer reviewed; Journal article, 2023)We consider the group (Ǧ, ∗)of unitized multiplicative functions in the incidence algebra of noncrossing partitions, where “∗” denotes the convolution operation. We introduce a larger group (Ǧ, ∗) of unitized functions ... 
On noncommutative stochastic exponentials
Curry, Charles Henry Alexander; EbrahimiFard, Kurusch; Patras, Frederic (Journal article; Peer reviewed, 2019)Using noncommutative shuffle algebra, we outline how the Magnus expansion allows to define explicit stochastic exponentials for matrixvalued continuous semimartingales and Stratonovich integrals. 
PostLie Magnus Expansion and BCHRecursion
AlKaabi, Mahdi J. Hasan; EbrahimiFard, Kurusch; Manchon, Dominique (Journal article; Peer reviewed, 2022) 
Relations between infinitesimal noncommutative cumulants
EbrahimiFard, Kurusch; de Jesus Celestino Rodr, Adrian; Perales Anaya, Daniel (Journal article; Peer reviewed, 2021)Boolean, free and monotone cumulants as well as relations among them, have proven to be important in the study of noncommutative probability theory. Quite notably, Boolean cumulants were successfully used to study free ... 
Renormalisation group for multiple zeta values
EbrahimiFard, Kurusch; Manchon, Dominique; Singer, Johannes; Zhao, Jianqang (Journal article; Peer reviewed, 2018)Calculating multiple zeta values at arguments of any sign in a way that is compatible with both the quasishuffle product as well as meromorphic continuation, is commonly referred to as the renormalisation problem for ... 
Shifted Substitution in NonCommutative Multivariate Power Series with a View Toward Free Probability
EbrahimiFard, Kurusch; Patra, Frédéric; Zambotti, Lorenzo; Tapia, Nikolas (Peer reviewed; Journal article, 2023)We study a particular group law on formal power series in noncommuting variables induced by their interpretation as linear forms on a suitable graded connected word Hopf algebra. This group law is leftlinear and is ... 
Shuffle group laws: applications in free probability
EbrahimiFard, Kurusch; Patras, Frederic (Peer reviewed; Journal article, 2019)Commutative shuffle products are known to be intimately related to universal formulas for products, exponentials and logarithms in group theory as well as in the theory of free Lie algebras, such as, for instance, the ... 
Tropical time series, iteratedsums signatures and quasisymmetric functions
EbrahimiFard, Kurusch; Tapia, Nikolas; Diehl, Joscha (Journal article; Peer reviewed, 2022) 
Universal Zero Dynamics: The SISO Case
EbrahimiFard, Kurusch; Gray, W. Steven; Schmeding, Alexander (Chapter, 2021)Given a singleinput, singleoutput (SISO) system with a ChenFliess series representation whose generating series has a well defined relative degree, it is shown that there is a notion of universal zero dynamics that ... 
What is a postLie algebra and why is useful in geometric integration
Curry, Charles Henry Alexander; EbrahimiFard, Kurusch; MuntheKaas, Hans (Journal article; Peer reviewed, 2018)We explain the notion of a postLie algebra and outline its role in the theory of Lie group integrators. 
Wick polynomials in noncommutative probability: A grouptheoretical approach
EbrahimiFard, Kurusch; Patras, Frédéric; Tapia, Nikolas; Zambotti, Lorenzo (Journal article; Peer reviewed, 2021) 
Zeroing the Output of Nonlinear Systems Without Relative Degree
EbrahimiFard, Kurusch; Gray, W. Steven; Schmeding, Alexander (Book, 2023)The goal of this paper is to establish some facts concerning the problem of zeroing the output of an inputoutput system that does not have relative degree. The approach taken is to work with systems that have ChenFliess ...