32 citations · 174 across the 33 of their papers we have counts for
39 papers
Weak Similarity Orbit of (log)-Self-Similar Markov Semigroups on the Euclidean Space
Pierre Patie, Rohan Sarkar
We start by identifying a class of pseudo-differential operators, generated by the set of continuous negative definite functions, that are in the weak similarity (WS) orbit of the…
A new class of solutions to the van Dantzig problem, the Lee-Yang property, and the Riemann hypothesis
T. Konstantopoulos, P. Patie, R. Sarkar
The purpose of this paper is to carry out an in-depth analysis of the intriguing van Dantzig problem which consists on characterizing the set of analytic characteristi…
Fluctuation theory of continuous-time skip-free downward Markov chains with applications to branching processes with immigration
R. Loeffen, P. Patie, J. Wang
We develop a new methodology for the fluctuation theory of continuous-time skip-free Markov chains, extending the recent work of Choi and Patie [5] for discrete-time skip-free Mark…
Jacobi processes with jumps as neuronal models: a first passage time analysis
Giuseppe D'Onofrio, Pierre Patie, Laura Sacerdote
To overcome some limits of classical neuronal models, we propose a Markovian generalization of the classical model based on Jacobi processes by introducing downwards jumps to descr…
Discrete self-similar and ergodic Markov chains
Laurent Miclo, Pierre Patie, Rohan Sarkar
The first aim of this paper is to introduce a class of Markov chains on which are discrete self-similar in the sense that their semigroups satisfy an invariance prop…
Non-local heat equations with moving boundary
Giacomo Ascione, Pierre Patie, Bruno Toaldo
In this paper we consider non-local (in time) heat equations on time-increasing parabolic sets whose boundary is determined by a suitable curve. We provide a notion of solution for…