20 citations · 25 across the 10 of their papers we have counts for
16 papers
Monte Carlo pricing under fast mean-reverting stochastic volatility: the multi-scale limit
Laurent Mertz, Olivier Pironneau
We compute $\E[(S_T-K)^+]$ by Monte Carlo for a scalar stochastic-volatility model with a fast mean-reverting factor of time scale $\eps$, for $\eps$ ranging from down to $10^{…
Improving Diffusion Generative Models via Truncated Karhunen--Loève Expansion
Yumeng Ren, Yaofang Liu, Aitor Artola +3
Pretrained diffusion models exhibit a well-known training-sampling mismatch, often attributed to exposure bias and related distribution-shift effects. We provide a quantitative int…
Constrained non-linear estimation and links with stochastic filtering
Louis-Pierre Chaintron, Laurent Mertz, Philippe Moireau +1
This article studies the problem of estimating the state variable of non-smooth subdifferential dynamics constrained in a bounded convex domain given some real-time observation. On…
An elementary approach based on variational inequalities for modelling a friction-based locomotion problem
Panyu Chen, Alvaro Mateos Gonzalez, Laurent Mertz
We propose an elementary proof based on a penalization technique to show the existence and uniqueness of the solution to a system of variational inequalities modelling the friction…
Computing the diffusivity of a particle subject to dry friction with colored noise
Josselin Garnier, Laurent Mertz
This paper considers the motion of an object subjected to dry friction and an external random force. The objective is to characterize the role of the correlation time of the extern…
Mortensen Observer for a class of variational inequalities -Lost equivalence with stochastic filtering approaches
L. P. Chaintron, Álvaro Mateos González, Laurent Mertz +1
We address the problem of deterministic sequential estimation for a nonsmooth dynamics in R governed by a variational inequality, as illustrated by the Skorokhod problem with a ref…
A piecewise deterministic Markov process approach modeling a dry friction problem with noise
Josselin Garnier, Ziyu Lu, Laurent Mertz
Understanding and predicting the dynamical properties of systems involving dry friction is a major concern in physics and engineering. It abounds in many mechanical processes, from…
Probing quantum effects with classical stochastic analogs
Rémi Goerlich, Giovanni Manfredi, Paul-Antoine Hervieux +2
We propose a method to construct a classical analog of an open quantum system, namely a single quantum particle confined in a potential well and immersed in a thermal bath. The cla…
Optimal protocols and universal time-energy bound in Brownian thermodynamics
Yoseline Rosales-Cabara, Giovanni Manfredi, Gabriel Schnoering +3
We propose an optimization strategy to control the dynamics of a stochastic system transferred from one thermal equilibrium to another and apply it experimentally to a Brownian par…
A control variate method driven by diffusion approximation
Josselin Garnier, Laurent Mertz
In this paper we examine a control variate estimator for a quantity that can be expressed as the expectation of a functional of a random process, that is itself the solution of a d…
Penalization of non-smooth dynamical systems with noise : ergodicity and asymptotic formulae for threshold crossings probabilities
Mathieu Lauriere, Laurent Mertz
The purpose of this paper is to prove ergodicity and provide asymptotic formulae for probabilities of threshold crossing related to smooth approximations of three fundamental nonli…
A Feynman-kac Formula Approach for Computing Expectations and Threshold Crossing Probabilities of Non-smooth Stochastic Dynamical Systems
Laurent Mertz, Georg Stadler, Jonathan Wylie
We present a computational alternative to probabilistic simulations for non-smooth stochastic dynamical systems that are prevalent in engineering mechanics. As examples, we target…
Asymptotic Analysis of Stochastic Variational Inequalities Modeling an Elasto-Plastic Problem with Vanishing Jumps
Alain Bensoussan, Hector Jasso Fuentes, Laurent Mertz
In a previous work by the first author with J. Turi (AMO, 08), a stochastic variational inequality has been introduced to model an elasto-plastic oscillator with noise. A major adv…
Degenerate Dirichlet Problems Related to the Ergodic Property of an Elasto-Plastic Oscillator Excited by a Filtered White Noise
Alain Bensoussan, Laurent Mertz
A stochastic variational inequality is proposed to model an elasto-plastic oscillator excited by a filtered white noise. We prove the ergodic properties of the process and characte…
Behavior of the plastic deformation of an elasto-perfectly-plastic oscillator with noise
Alain Bensoussan, Laurent Mertz
Earlier works in engineering, partly experimental, partly computational have revealed that asymptotically, when the excitation is a white noise, plastic deformation and total defor…
An analytic approach to the ergodic theory of stochastic variational inequalities
Alain Bensoussan, Laurent Mertz
In an earlier work made by the first author with J. Turi (Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators, AMO, 2008), the solution of…