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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The blockchain folk theorem.

Blockchains, Cryptocurrency mining Stochastic analysis Software upgrades Computable general equilibrium models, Markov processes, Nash equilibrium, Peer-to-peer architecture Computer networks

Contributions to the study of biological models, functional inequalities, and random matrices.

Biostatistics, Biostatistique, Compartmental models, Diffusion processes, Entropie, Entropy, Functional inequalities, Inégalités fonctionnelles, Markov processes, Mixed effects models, Modèles compartimentaux, Modèles à effets mixtes, Pharmacologie de population, Population pharmacology, Processus de Markov, Processus de diffusion, Spectres de matrices aléatoires, Spectrum of random matrices

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

Recursive computation of the invariant distribution of Markov and Feller processes.

Ergodic theory, Invariant measures, Limit theorem, Markov processes, Stochastic approximation

Martingale driven BSDEs, PDEs and other related deterministic problems.

Backward stochastic differential equation, Cadlag martingale, Decoupled mild solutions, Markov processes, Martingale problem, Pseudo-PDE

BSDEs with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations. Part II: Decoupled mild solutions and Examples.

Backward stochastic differential equation, Decoupled mild solutions, Markov processes, Martingale problem, Pseudo-PDE

Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations.

Backward stochastic differential equation, Markov processes, Martingale problem, Pseudo-PDE

A note on time-dependent additive functionals.

Additive functionals, Covariation, Markov processes

Optimization of the availability of multi-states systems under uncertainty.

Complex systems, Intervalles, Intervals, Maintainability, Markov processes, Mathematical models, Mathematical optimization, Probabilities, Probabilités des états de fonctionnement, Reliability, Systems availability, Systems engineering, Système multi-états (MSS), Uncertainty