2 citations · 5 across the 13 of their papers we have counts for
13 papers
q-Algebraic Equations, their power series solutions, and the asymptotic behavior of their coefficients
Ph. Barbe, J. Cano, P. Fortuny Ayuso +1
We give a systematic study of q-algebraic equations. The questions of existence, uniqueness and regularity of the solutions are solved in the space of grid-based Hahn series. The r…
Some Tauberian theory for the q-Lagrange inversion
Ph. Barbe, W. P. McCormick
We consider formal power series defined through the functional q-equation of the q-Lagrange inversion. Under some assumptions, we obtain the asymptotic behavior of the coefficients…
On q-algebraic equations and their power series solutions
Ph. Barbe, W. P. McCormick
We study the existence of formal power series solutions to q-algebraic equations. When a solution exists, we give a sufficient condition on the equation for this solution to have a…
q-Catalan bases and their dual coefficients
Ph. Barbe, W. P. McCormick
We define q-Catalan bases which are a generalization of the q-polynomials z^n(z,q)_n. The determination of their dual bases involves some q-power series termed dual coefficients. W…
Ruin probabilities in tough times - Part 2 - Heavy-traffic approximation for fractionally differentiated random walks in the domain of attraction of a nonGaussian stable distribution
Ph. Barbe, W. P. McCormick
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for processes which encompass the fractionally differentiated random walk as well as…
Ruin probabilities in tough times - Part 1 - Heavy-traffic approximation for fractionally integrated random walks in the domain of attraction of a nonGaussian stable distribution
Ph. Barbe, W. P. McCormick
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for process which encompass the fractionally integrated random walk as well as some F…