Hélène Guérin
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View article: Optimal vaccination policy to prevent endemicity: a stochastic model
Optimal vaccination policy to prevent endemicity: a stochastic model Open
We examine here the effects of recurrent vaccination and waning immunity on the establishment of an endemic equilibrium in a population. An individual-based model that incorporates memory effects for transmission rate during infection and …
View article: Measure estimation on a manifold explored by a diffusion process
Measure estimation on a manifold explored by a diffusion process Open
From the observation of a diffusion path $(X_t)_{t\in [0,T]}$ on a compact connected $d$-dimensional manifold $\mathcal{M}$ without boundary, we consider the problem of estimating the stationary measure $μ$ of the process. Wang and Zhu (20…
View article: On the limit law of the superdiffusive elephant random walk
On the limit law of the superdiffusive elephant random walk Open
When the memory parameter of the elephant random walk is above a critical threshold, the process becomes superdiffusive and, once suitably normalised, converges to a non-Gaussian random variable. In a recent paper by the three first author…
View article: Optimal withdrawals in a general diffusion model with control rates subject to a state-dependent upper bound
Optimal withdrawals in a general diffusion model with control rates subject to a state-dependent upper bound Open
We consider a classical stochastic control problem in which a diffusion process is controlled by a withdrawal process up to a termination time. The objective is to maximize the expected discounted value of the withdrawals until the first-p…
View article: Elephant polynomials
Elephant polynomials Open
In this note, we study a family of polynomials that appear naturally when analysing the characteristic functions of the one-dimensional elephant random walk. These polynomials depend on a memory parameter $p$ attached to the model. For cer…
View article: A fixed-point equation approach for the superdiffusive elephant random walk
A fixed-point equation approach for the superdiffusive elephant random walk Open
We study the elephant random walk in arbitrary dimension $d\geq 1$. Our main focus is the limiting random variable appearing in the superdiffusive regime. Building on a link between the elephant random walk and Pólya-type urn models, we pr…
View article: Optimal Vaccination Policy to Prevent Endemicity: A Stochastic Model
Optimal Vaccination Policy to Prevent Endemicity: A Stochastic Model Open
We examine here the effects of recurrent vaccination and waning immunity on the establishment of an endemic equilibrium in a population. An individual-based model that incorporates memory effects for transmission rate during infection and …
View article: Strong uniform convergence of Laplacians of random geometric and directed kNN graphs on compact manifolds
Strong uniform convergence of Laplacians of random geometric and directed kNN graphs on compact manifolds Open
Consider $n$ points independently sampled from a density $p$ of class $\mathcal{C}^2$ on a smooth compact $d$-dimensional sub-manifold $\mathcal{M}$ of $\mathbb{R}^m$, and consider the generator of a random walk visiting these points accor…
View article: Strong uniform convergence of Laplacians of random geometric and directed kNN graphs on compact manifolds
Strong uniform convergence of Laplacians of random geometric and directed kNN graphs on compact manifolds Open
Consider $n$ points independently sampled from a density $p$ of class $\mathcal{C}^2$ on a smooth compact $d$-dimensional sub-manifold $\mathcal{M}$ of $\mathbb{R}^m$, and consider the generator of a random walk visiting these points accor…
View article: Comportement en temps long et étude de modèles probabilistes pour des phénomènes physiques, biologiques et actuariels
Comportement en temps long et étude de modèles probabilistes pour des phénomènes physiques, biologiques et actuariels Open
This document is an overview of my works on different probabilistic models for various applications, always with the aim of studying carefully the behavior and properties of the underlying process.First, the question of the dependence on t…
View article: Long time behavior of telegraph processes under convex potentials
Long time behavior of telegraph processes under convex potentials Open
We study the long-time behavior of variants of the telegraph process with position-dependent jump rates, which result in a monotone gradient-like drift towards the origin. We compute their invariant laws and obtain, via probabilistic coupl…
View article: On the Laplace transform of perpetuities with thin tails
On the Laplace transform of perpetuities with thin tails Open
We consider the random variables R which are solutions of the distributional equation R L = MR+Q, where (Q, M) is independent of R and |M | � 1. Goldie and Grübel showed that the tails of R are no heavier than exponential. Alsmeyer and al …
View article: Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view
Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view Open
We study the distribution E x [exp(- q ∫ 0 t 1 ( a , b ) ( X s )d s ); X t ∈ d y ], where -∞ ≤ a < b < ∞, and where q , t > 0 and x ∈ R for a spectrally negative Lévy process X . More precisely, we identify the Laplace transform with respe…
View article: On the distribution of cumulative Parisian ruin
On the distribution of cumulative Parisian ruin Open
We introduce the concept of cumulative Parisian ruin, which is based on the time spent in the red by the underlying surplus process. Our main result is an explicit representation for the distribution of the occupation time, over a finite-t…