4 papers
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 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…