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Optimal Control of Infinite-Dimensional Piecewise Deterministic Markov Processes: A BSDE Approach. Application to the Control of an Excitable Cell Membrane

Applied mathematics & optimization, 2021-10, Vol.84 (2), p.1549-1603

2021

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Exact Simulation of the Jump Times of a Class of Piecewise Deterministic Markov Processes

Journal of scientific computing, 2018-06, Vol.75 (3), p.1776-1807

2018

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Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants

Physical review. E, 2022-11, Vol.106 (5), Article 054410

2022

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A contrast estimator for completely or partially observed hypoelliptic diffusion

Stochastic processes and their applications, 2012-07, Vol.122 (7), p.2521-2552

2012

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Minimal time spiking in various ChR2-controlled neuron models

Journal of mathematical biology, 2018-02, Vol.76 (3), p.567-608

2018

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Optimal Transportation Problem by Stochastic Optimal Control

SIAM journal on control and optimization, 2008-01, Vol.47 (3), p.1127-1139

2008

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Duality theorem for the stochastic optimal control problem

Stochastic processes and their applications, 2006-12, Vol.116 (12), p.1815-1835

2006

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Iterated Stochastic Processes: Simulation and Relationship with High Order Partial Differential Equations

Methodology and computing in applied probability, 2017-03, Vol.19 (1), p.121-149

2017

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Simulation of SPDEs for Excitable Media Using Finite Elements

Journal of scientific computing, 2015-10, Vol.65 (1), p.171-195

2015

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Length of clustering algorithms based on random walks with an application to neuroscience

Chaos, solitons and fractals, 2012-05, Vol.45 (5), p.629-639

2012

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Averaging for a Fully Coupled Piecewise-Deterministic Markov Process in Infinite Dimensions

Advances in applied probability, 2012-09, Vol.44 (3), p.749-773

2012

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Reduction of stochastic conductance-based neuron models with time-scales separation

Journal of computational neuroscience, 2012-04, Vol.32 (2), p.327-346

2012

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Asymptotic expansion and central limit theorem for multiscale piecewise-deterministic Markov processes

Stochastic processes and their applications, 2012-06, Vol.122 (6), p.2292-2318

2012

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Spatio-temporal hybrid (PDMP) models: Central limit theorem and Langevin approximation for global fluctuations. Application to electrophysiology

Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, 2015-05, Vol.21 (2), p.647-696

2015

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Limit theorems for infinite-dimensional piecewise deterministic Markov processes. Applications to stochastic excitable membrane models

Electronic journal of probability, 2012, Vol.17 (none)

2012

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Ergodicity and limit theorems for degenerate diffusions with time periodic drift. Application to a stochastic Hodgkin−Huxley model

Probability and statistics, 2016, Vol.20, p.527-554

2016

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THINNING AND MULTILEVEL MONTE CARLO METHODS FOR PIECEWISE DETERMINISTIC (MARKOV) PROCESSES WITH AN APPLICATION TO A STOCHASTIC MORRIS–LECAR MODEL

Advances in applied probability, 2020-03, Vol.52 (1), p.138-172

2020

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Diffusion approximation of birth–death processes: Comparison in terms of large deviations and exit points

Statistics & probability letters, 2010-07, Vol.80 (13), p.1121-1127

2010

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Optimal control of infinite-dimensional piecewise deterministic Markov processes and application to the control of neuronal dynamics via Optogenetics

Networks and heterogeneous media, 2017-09, Vol.12 (3), p.417-459

2017

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Deterministic and Stochastic FitzHugh–Nagumo Systems

Stochastic Biomathematical Models, p.175-186

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Intrinsic variability of latency to first-spike

Biological cybernetics, 2010-07, Vol.103 (1), p.43-56

2010

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Stochastic Representation of Tau Functions With an Application to the Korteweg-De Vries Equation

Communications on stochastic analysis, 2018-08, Vol.12 (1)

2018

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Martingale Structure of Skorohod Integral Processes

The Annals of probability, 2006-05, Vol.34 (3), p.1217-1239

2006

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Averaging for a Fully Coupled Piecewise-Deterministic Markov Process in Infinite Dimensions

Advances in applied probability, 2012-09, Vol.44 (3), p.749-773

2012

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A characterization of reciprocal processes via an integration by parts formula on the path space

Probability theory and related fields, 2002-05, Vol.123 (1), p.97-120

2002

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Optimal Control of Infinite-Dimensional Piecewise Deterministic Markov Processes: A BSDE Approach. Application to the Control of an Excitable Cell Membrane

Exact Simulation of the Jump Times of a Class of Piecewise Deterministic Markov Processes

Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants

A contrast estimator for completely or partially observed hypoelliptic diffusion

Minimal time spiking in various ChR2-controlled neuron models

Optimal Transportation Problem by Stochastic Optimal Control

Duality theorem for the stochastic optimal control problem

Iterated Stochastic Processes: Simulation and Relationship with High Order Partial Differential Equations

Simulation of SPDEs for Excitable Media Using Finite Elements

Length of clustering algorithms based on random walks with an application to neuroscience

Averaging for a Fully Coupled Piecewise-Deterministic Markov Process in Infinite Dimensions

Reduction of stochastic conductance-based neuron models with time-scales separation

Asymptotic expansion and central limit theorem for multiscale piecewise-deterministic Markov processes

Spatio-temporal hybrid (PDMP) models: Central limit theorem and Langevin approximation for global fluctuations. Application to electrophysiology

Limit theorems for infinite-dimensional piecewise deterministic Markov processes. Applications to stochastic excitable membrane models

Ergodicity and limit theorems for degenerate diffusions with time periodic drift. Application to a stochastic Hodgkin−Huxley model

THINNING AND MULTILEVEL MONTE CARLO METHODS FOR PIECEWISE DETERMINISTIC (MARKOV) PROCESSES WITH AN APPLICATION TO A STOCHASTIC MORRIS–LECAR MODEL

Diffusion approximation of birth–death processes: Comparison in terms of large deviations and exit points

Optimal control of infinite-dimensional piecewise deterministic Markov processes and application to the control of neuronal dynamics via Optogenetics

Deterministic and Stochastic FitzHugh–Nagumo Systems

Intrinsic variability of latency to first-spike

Stochastic Representation of Tau Functions With an Application to the Korteweg-De Vries Equation

Martingale Structure of Skorohod Integral Processes

Averaging for a Fully Coupled Piecewise-Deterministic Markov Process in Infinite Dimensions

A characterization of reciprocal processes via an integration by parts formula on the path space

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