39 citations · 107 across the 13 of their papers we have counts for
14 papers
A Classification of Asymptotic Behaviors of Green Functions of Random Walks in the Quadrant
Irina Ignatiouk-Robert
This paper investigates the asymptotic behavior of Green functions associated to partially homogeneous random walks in the quadrant . There are four possible distributions f…
Asymptotics of the Green function of killed random walks in a cone of
Irina Ignatiouk-Robert
In this paper, we obtain the exact asymptotic behavior of Green functions of homogeneous random walks in killed at the first exit from and open cone of . Our approach…
Reflected random walks and unstable Martin boundary
Irina Ignatiouk-Robert, Irina Kourkova, Kilian Raschel
We introduce a family of two-dimensional reflected random walks in the positive quadrant and study their Martin boundary. While the minimal boundary is systematically equal to a un…
Martin boundary of a killed non-centered random walk in a general cone
Irina Ignatiouk-Robert
We investigate Martin boundary for a non-centered random walk on killed up on the time of the first exit from a convex cone with a vertex at . The…
Harmonic functions of random walks in a semigroup via ladder heights
Irina Ignatiouk-Robert
We investigate harmonic functions and the convergence of the sequence of ratios for a random walk on a countable group killed up o…
Explicit Lyapunov functions and estimates of the essential spectral radius for Jackson networks
Irina Ignatiouk-Robert, Danielle Tibi
A family of explicit Lyapunov function for positive recurrent Markovian Jackson network is constructed. With this result we obtain explicit estimates of the tail distribution of th…