Patrimony

The Louis Bachelier Group's patrimony has been defined as all the publications produced by academic researchers thanks to Group funding (ILB, FdR, IEF, Labex) or via the use of EquipEx data (BEDOFIH, EUROFIDAI).


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Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT.

Central limit theorem, Entropic-Wasserstein barycenters, Monge-Ampère equations and systems

On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group.

Brownian Motion, Central Limit Theorem, Heat kernel, Heisenberg group, Logarithmic Sobolev inequality, Poincaré inequality, Random Walk

From Boltzmann to random matrices and beyond.

Boltzmann, Central limit theorem, Circular law, Collective phenomena, Coulomb gas, Diffusion processes, Electrostatics, Entropy, Equilibrium measure, Fisher information, Free probability, Ginibre ensemble, Interacting Particle Systems, Large Deviations Principle, Markov processes, Mean-field interaction, Potential theory, Random matrices, Riesz kernel, Shannon, Singular repulsion, Voiculescu

Statistical inference for a partially observed interacting system of Hawkes processes.

Central limit theorem, Graphe d'interaction, Inférence statistique, Interaction graph, Limite de champ moyenne, Mean field limit, Multivariate Hawkes processes, Particules à interaction stochastique, Processus Hawkes multivarié, Processus ponctuels, Statistical inference, Stochastic interacting particles

Coupling Importance Sampling and Multilevel Monte Carlo using Sample Average Approximation.

Central limit theorem, Importance Sampling, Multilevel Monte Carlo, Uniform strong large law of numbers, Variance reduction

Asymptotic study of stochastic algorithms and computation of Parisian options prices.

Algorithmes tronqués, Approximation stochastique, Central limit theorem, Inversion numérique, Laplace transforms, Numerical inversion, Options parisiennes, Parisian options, Stochastic approximation, Théorème centrale limite, Transformées de Laplace, Truncated algorithms

Asymptotic normality of randomly truncated stochastic algorithms.

Central limit theorem, Martingale arrays, Randomly truncated stochastic algorithms, Stochastic approximation

Asymptotic study of stochastic algorithms and computation of Parisian options prices.

Algorithmes tronqués, Approximation stochastique, Central limit theorem, Inversion numérique, Laplace transforms, Numerical inversion, Options parisiennes, Parisian options, Stochastic approximation, Théorème central limite, Transformés de Laplace, Troncated algorithms

Invariant measure of duplicated diffusions and application to Richardson–Romberg extrapolation.

Asymptotic flatness, Central Limit Theorem, Confluence, Ergodic diffusion, Euler scheme, Gradient System, Hypoellipticity, Invariant measure, Lyapunov exponent, Optimal transport, Richardson-Romberg extrapolation, Two-point motion

Limit theorems for weighted and regular Multilevel estimators.

Central Limit Theorem, Euler scheme, Law of large numbers, Multilevel Monte Carlo methods, Nested Monte Carlo, Richardson- Romberg extrapolation

A mixed-step algorithm for the approximation of the stationary regime of a diffusion.

Central Limit Theorem, Ergodic diffusion, Euler scheme, Poisson equation, Stationary process, Steady regime, Stochastic differential equation

Importance Sampling and Statistical Romberg method.

Central limit theorem, Euler scheme, Heston model, Robbins-Monro, Statistical Romberg method, Stochastic algorithm, Variance reduction