6 papers · 1 filter
Delayed logistic equation as a limit of long memory Markov chains
Eldon Barros, Dirk Erhard, Tertuliano Franco +1
We introduce and analyze a long-memory continuous-time Markov chain on whose jump mechanism depends explicitly on a state in the past. From the present state …
The Most General Brownian Motion on the Line and on Two Closed Half-Lines
Dirk Erhard, Tertuliano Franco, Wanessa Muricy
In the 1950s, W. Feller characterized the most general Brownian motion on the closed half-line. He showed that any such process is a mixture of reflected, sticky, and killed Browni…
Superdiffusive Scaling Limits for the Symmetric Exclusion Process with Slow Bonds
Dirk Erhard, Tertuliano Franco, Tiecheng Xu
In \cite{fgn1}, the hydrodynamic limit in the diffusive scaling of the symmetric simple exclusion process with a finite number of slow bonds of strength has been studied.…
A strong large deviation principle for the empirical measure of random walks
Dirk Erhard, Tertuliano Franco, Joedson de Jesus Santana
In this article we show that the empirical measure of certain continuous time random walks satisfies a strong large deviation principle with respect to a topology introduced in~\ci…
A Functional Central Limit Theorem for the General Brownian Motion on the Half-Line
Dirk Erhard, Tertuliano Franco, Milton Jara +1
In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their ge…
Uniqueness and tube property for the Swiss cheese large deviations
Julien Poisat, Dirk Erhard
We consider the simple random walk on the Euclidean lattice, in three dimensions and higher, conditioned to visit fewer sites than expected, when the deviation from the mean scales…