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12
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Introduction
Current institution
Education
January 2007 - June 2011
University of Tours
Field of study
- Mathematics
September 2004 - August 2006
October 2003 - August 2004
Publications
Publications (12)
This article shows the geometric decay rate of Euler-Maruyama scheme for one-dimensional stochastic differential equation towards its invariant probability measure under total variation distance. Firstly, the existence and uniqueness of invariant probability measure and the uniform geometric ergodicity of the chain are studied through introduction...
Let $ (Z_{n})_{n\geq 0} $ be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-$1$ distance for the process $ (Z_{n})_{n\geq 0} $, which completes a result of Grama et al. [Stochastic Process. Appl., 127(4), 1255-1281, 2017]. Moreover, an e...
Let $(Z_{n})_{n\geq 0}$ be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-$1$ distance for the process $(Z_{n})_{n\geq 0}$, which completes a result of Grama et al. [Stochastic Process. Appl., 127(4), 1255-1281, 2017]. Moreover, an expon...
Let $\{Z_{1,n} , n\geq 0\}$ and $\{Z_{2,n}, n\geq 0\}$ be two supercritical branching processes in different random environments, with criticality parameters $\mu_1$ and $\mu_2$ respectively. It is known that $\frac{1}{n} \ln Z_{1,n} \rightarrow \mu_1$ and $\frac{1}{m} \ln Z_{2,m} \rightarrow \mu_2$ in probability as $m, n \rightarrow \infty.$ In t...
Suppose that $(Z_n)_{n\geq0}$ is a supercritical branching process in independent and identically distributed random environment. We study the positive tail function of the scaled growth rate for $(Z_n)_{n\geq0}$ and establish an Hoeffding type inequality.
Let (Ω, F, P) be a probability space and E be a finite set. Assume that X = (Xn) is an irreducible and aperiodic Markov chain, defined on (Ω, F, P), with values in E and with transition probability P = pi,j i,j. Let (F (i, j, dx))i,j∈E be a family of probability measures on R. Consider a semi-markovian chain (Yn, Xn) on R × E with transition probab...
The purpose of this thesis is to study the survival probability of a branching process in markovian random environment and expand in this framework some known results which have been developed for a branching processus in i.i.d. random environment, the core of the study is based on the use of the local limit theorem for a centered random walk (Sn)n...
