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Guillaume Broux-Quemerais,Sarah Kaakai, Anis Matoussi,Wissal Sabbagh

Probability, Uncertainty and Quantitative Risk 2024年第2期9卷 149-180页

作者： Guillaume Broux-Quemerais Sarah Kaakarl Anis Matoussi Wissal Sabbagh laboratoire manceau de mathematiques&fr cnrs no 2962 Institut du Risque et de I'AssuranceLeMansUniversityFrance Centre de Mathématiques Appliquees(CMAP) CNRSEcole polytechniqueInstitut Polytechnique de Paris91120 PalaiseauFrance

In this paper,we present a probabilistic numerical method for a class of forward utilities in a stochastic factor *** this purpose,we use the representation of forward utilities using the ergodic Backward Stochastic Differential Equations(eBSdes)introduced by Liang and Zariphopoulou in[27].We establish a connection between the solution of the ergodic BSde and the solution of an associated BSde with random terminal time T,defined as the hitting time of the positive recurrent stochastic *** viewpoint based on BSdes with random horizon yields a new characterization of the ergodic cost^which is a part of the solution of the *** particular,for a certain class of eBSdes with quadratic generator,the Cole-Hopf transformation leads to a semi-explicit representation of the solution as well as a new expression of the ergodic cost>.The latter can be estimated with Monte Carlo *** also propose two new deep learning numerical schemes for ***,we present numerical results for different examples of eBSdes and forward utilities together with the associated investment strategies.

关键词： deep leaming scheme Forward utilities Ergodic BSdes Markovian solution deep learning algorithm

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On approximation of BSde and multi-step MLE-processes

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Probability, Uncertainty and Quantitative Risk 2016年第1期1卷 86-107页

作者： Yu A.Kutoyants laboratoire manceau des mathematiques Universite du Maine Le MansFrance and National Research University“MPEI”MoscowRussia

We consider the problem of approximation of the solution of the backward stochastic differential equations in Markovian *** suppose that the forward equation depends on some unknown finite-dimensional *** approximation is based on the solution of the partial differential equations and multi-step estimator-processes of the unknown *** the model of observations of the forward equation we take a diffusion process with small *** we establish a lower bound on the errors of all approximations and then we propose an approximation which is asymptotically efficient in the sense of this *** obtained results are illustrated on the example of the Black and Scholes model.

关键词： Backward stochastic differential equation Parameter estimation Multi-step MLE-process Small noise Black and Scholes model

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Cavity-based photoconductive sources for real-time terahertz imaging

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Photonics Research 2020年第6期8卷 858-863页

作者： J.HAWECKER V.PISTORE A.MINASYAN K.MAUSSANG J.PALOMO I.SAGNES J.-M.manceau R.COLOMBELLI J.TIGNON J.MANGENEY AND S.S.DHILLON laboratoire de Physique de I'Ecole normale superieure ENSUniversite PSLCNRSSorbonne UniversiteUniversite de ParisF-75005 ParisFrance i2S 28-30 rue Jean Perrin 33608 PessacFrance Centre de Nanosciences et de Nanotechnologies(C2N) CNRS UMR 9001Universite Paris-Saclay91120 PalaiseauFrance Institut d'Electronique et des Systemes CNRS(UMR 5214)Univ Montpellier860 rue de Saint-Priest34095 Montpellier Cedex 5France

Optically driven photoconductive switches are one of the predominant sources currently used in terahertz im-aging ***,owing to their low average powers,only raster-based images can be taken,resulting in slow *** this work,we show that by placing a photoconductive switch within a cavity,we are able to generate absolute average THz powers of 181μW with the frequency of the THz emission centered at 1.5 THz-specifications ideally adapted to applications such as non-destructive *** cavity is based on a metal-insulator-metal structure that permits an en hancement of the average power by almost 1 order of magnitude compared to a standard structure,while conserving a broadband spectral *** demonstrate proof-of-principle real-time imaging using this source,with the broadband spectrum permitting to eliminate strong diffraction artifacts.

关键词： photoconductive sources cavity

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