The uniform CLT for the empirical estimator of countable state space semi-Markov kernels indexed by functions with appli...
International audience
Programmation dynamique
Le but de ce cours est d'introduire le principe de programmation dynamique pour les problèmes de consommation et investissement optimales. Plus précisément dans ce cours on étudie le problème de consommation optimale en temps discret. On montre le principe de programmation dynamique dans ce cas et on obtient les équation de Bellman. Ensuite, on con...
Large population limit of the spectrum of killed birth-and-death processes
We consider a general class of birth-and-death processes with state space {0, 1, 2, 3,. . .} which describes the size of a population going eventually to extinction with probability one. We obtain the complete spectrum of the generator of the process killed at 0 in the large population limit, that is, we scale the process by a parameter K, and take...
Modèles Mathématiques Statiques de Marchés Financiers
Le but de ce cours est d'introduire les méthodes mathématiques de la finance. En particulier, nous étudions le modèle d'équilibre des Actifs Financièrs. Puis, on étudions la notion l'efficience des marchés. Comme une application on considère le modèle de Grossman-Stiglits.
Kinetic time-inhomogeneous Lévy-driven model
We study a one-dimensional kinetic stochastic model driven by a Lévy process with a non-linear time-inhomogeneous drift. More precisely, the process $(V,X)$ is considered, where $X$ is the position of the particle and its velocity $V$ is the solution of a stochastic differential equation with a drift of the form $t^{-\beta}F(v)$. The driving proces...
Introducing smooth amnesia to the memory of the Elephant Random Walk
This paper is devoted to the asymptotic analysis of the amnesic elephant random walk (AERW) using a martingale approach. More precisely, our analysis relies on asymptotic results for multidimensional martingales with matrix normalization. In the diffusive and critical regimes, we establish the almost sure convergence and the quadratic strong law fo...
An Introduction to Singular Stochastic PDEs / An Introduction to Singular Stochastic PDEs: Allen–Cahn Equations, Metasta...
Stochastic partial differential equations (SPDEs) model the evolution in time of spatially extended systems subject to a random driving. Recent years have witnessed tremendous progress in the theory of so-called singular SPDEs. These equations feature a singular, distribution-valued driving term, a typical example being spacetime white noise, which...
Notes on means, medians and Gaussian tails
In the course of thinking about Gaussian concentration bounds for X − E(X), we arrived at the basic question of replacing E(X) by a median of X. Not surprinsingly, having a Gaussian concentration bound for X about its mean is equivalent to having it for any of its median. The question is: Can we find simple relations between the involved constants?...
Blockchain mining in pools: Analyzing the trade-off between profitability and ruin
The resource-consuming mining of blocks on a blockchain equipped with a proof of work consensus protocol bears the risk of ruin, namely when the operational costs for the mining exceed the received rewards. In this paper we investigate to what extent it is of interest to join a mining pool that reduces the variance of the return of a miner for a sp...
Quasi-compactness criterion for strong Feller kernels with an application to quasi-stationary distributions
The aim of this note is to provide a sufficient criterion for the quasi-compactness of positive operators on $L^\infty$ type spaces. We provide applications to the theory of quasi-stationary distributions.
