22 citations · 43 across the 10 of their papers we have counts for
10 papers
Elephant polynomials
Hélène Guérin, Lucile Laulin, Kilian Raschel
In this note, we study a family of polynomials that appear naturally when analysing the characteristic functions of the one-dimensional elephant random walk. These polynomials depe…
Logarithmic terms in discrete heat kernel expansions in the quadrant
Andrew Elvey-Price, Andreas Nessmann, Kilian Raschel
In the context of lattice walk enumeration in cones, we consider the number of walks in the quarter plane with fixed starting and ending points, prescribed step-set and given lengt…
Random Walks in the High-Dimensional Limit II: The Crinkled Subordinator
Zakhar Kabluchko, Alexander Marynych, Kilian Raschel
A crinkled subordinator is an -valued random process which can be thought of as a version of the usual one-dimensional subordinator with each out of countably many jumps be…
Multivariate multiplicative functions of uniform random vectors in large integer domains
Zakhar Kabluchko, Oleksandr Marynych, Kilian Raschel
For a wide class of sequences of integer domains , , we prove distributional limit theorems for , w…
Harmonic functions for singular quadrant walks
Viet Hung Hoang, Kilian Raschel, Pierre Tarrago
We consider discrete (time and space) random walks confined to the quarter plane, with jumps only in directions with and small negative jumps, i.e., $i,j \geq…
A dual skew symmetry for transient reflected Brownian motion in an orthant
Sandro Franceschi, Kilian Raschel
We introduce a transient reflected Brownian motion in a multidimensional orthant, which is either absorbed at the apex of the cone or escapes to infinity. We address the question o…