255 citations · 949 across the 71 of their papers we have counts for
4 papers · 2 filters
Total variation estimates for the TCP process
Jean-Baptiste Bardet, Alejandra Christen, Arnaud Guillin +2
The TCP window size process appears in the modeling of the famous Transmission Control Protocol used for data transmission over the Internet. This continuous time Markov process ta…
Deviation inequalities, Moderate deviations and some limit theorems for bifurcating Markov chains with application
Valère Bitseki Penda, Hacène Djellout, Arnaud Guillin
First, under a geometric ergodicity assumption, we provide some limit theorems and some probability inequalities for the bifurcating Markov chains (BMC). The BMC model was introduc…
Central limit theorems for additive functionals of ergodic Markov diffusions processes
Patrick Cattiaux, Djalil Chafai, Arnaud Guillin
We revisit functional central limit theorems for additive functionals of ergodic Markov diffusion processes. Translated in the language of partial differential equations of evoluti…
Degenerate Fokker-Planck Equations : Bismut Formula, Gradient Estimate and Harnack Inequality
Arnaud Guillin, Feng-Yu Wang
By constructing successful couplings for degenerate diffusion processes, explicit derivative formula and Harnack type inequalities are presented for solutions to a class of degener…