Samuel HERRMANN

Research

Main topic: My research framework concerns the analysis of stochastic dfferential equations.
1. Asymptotic analysis related to the study of certain stochastic processes. This research area includes the study of large deviation phenomena for nonlinear stochastic processes such as self-attracting diffusions (driven by their own law), the analysis of diffusions perturbed by a periodic signal (highlighting stochastic resonance), long-time behavior of long-memory diffusions, and the study of chaos propagation in large interacting particle systems (solutions of stochastic differential equations). These studies are connected to problems arising from climate science, biology, and financial modeling.
2. Stochastic algorithms (simulation of passage time or exit time for diffusion processes).

Overview

PhD in 2001 (University of Nancy 1, under Bernard Roynette): Study of diffusion processes.
HDR in 2009: Asymptotic analysis related to certain stochastic processes

• 2011 - present: University of Burgundy (Dijon, France), professor
• 2002 - 2011: Université de Lorraine (Ecole des Mines de Nancy), assistant professor
• 2008 - 2009: On leave at INRIA (Nancy, France)
• 2001 - 2002: Postdoctoral position (DFG fellowship) at the Technical university of Berlin, Germany.

Published articles

• A singular large deviations phenomenon (avec M. Gradinaru et B. Roynette) document postscript
  Annales de l’Institut Henri Poincaré 37 (2001) no.5, pp 555—580
• Phénomène de Peano et Grandes Déviations pdf
  Comptes Rendus de l’Académie des Sciences 332 (2001) no.11
• Barrier crossings characterize stochastic resonance (avec P. Imkeller) pdf
  Stochastics and Dynamics 2, no.3 (2002), pp 413-436
• Boundedness and convergence of some self-attracting diffusions (avec B. Roynette) pdf
  Mathematische Annalen 325, no.1 (2003), pp 81-96
• Système de processus auto-stabilisants pdf
  Dissertationes Mathematicae 414 (2003) 49 pages.
• Rate of convergence of some self-attracting diffusions (avec M. Scheutzow) pdf
  Stochastic Processes and their Applications 111, no.1 (2004), pp 41-55.
• The exit problem for diffusions with time-periodic drift and stochastic resonance. (avec P. Imkeller) pdf
  Annals of Applied Probability 15, no. 1A, (2005), pp 39—68
• Transition times and stochastic resonance for multidimensional diffusions with time periodic drift : a large deviations approach. (avec P. Imkeller et D. Peithmann). pdf
  Annals of Applied Probability 16, no. 4 (2006), pp 1851—1892
• Large deviations and a Kramers’ type law for self-stabilizing diffusions (avec P. Imkeller et D. Peithmann). pdf
  Annals of Applied Probability 18, no. 4 (2008), pp 1379—1423
• Non uniqueness of stationary measures for self-stabilizing diffusions (avec J. Tugaut) pdf
  Stochastic Processes & Their Applications 120, no. 7 (2010), pp. 1215-1246
• From persistant random walk to the telegrapg noise (avec P. Vallois) pdf
  Stochastics and Dynamics 10, no. 2 (2010), pp. 161—196
• Stationary measures for self-stabilizing diffusions : asymptotic analysis in the small noise limit (avec J. Tugaut) pdf
  Elect. Journ. Probab. 15 (2010), pp. 2087-2116.
• Self-stabilizing processes : uniqueness problem for stationary measures and convergence rate in the small noise limit (avec J. Tugaut) pdf
  ESAIM P&S 16 (2012), pp. 277-305.
• Hitting time for Bessel processes - Walk on moving spheres algorithm (WOMS) (avec M. Deaconu) pdf
  Ann. Appl. Probab. 23 (2013), no. 6, 2259–2289.
• Persistent random walks, variable length Markov chains and piecewise deterministic Markov processes avec P. Cénac, B. Chauvin et P. Vallois pdf
  Markov Process. Related Fields 19 (2013), no. 1, 1–50.
• Statistics of transitions for Markov chains with periodic forcing (with D. Landon) pdf
  Stoch. Dyn. 15 (2015), no. 4, 30 pp.
• The first-passage time of the Brownian motion to a curved boundary: an algorithmic approach (with E. Tanré) pdf
  SIAM Journal on Scientific Computing, 38 (2016), no. 1, A196–A215.
• Mean-field limit versus small-noise limit for some interacting particle systems (with J. Tugaut) pdf Communications on Stochastic Analysis, Vol. 10, No. 1 (2016) 39-55
• The walk on moving spheres: A new tool for simulating Brownian motion's exit time from a domain (with M. Deaconu and S. Maire) pdf
  Mathematics and Computers in Simulation, Vol. 135 (2017), pp. 28--38.
• Simulation of hitting times for Bessel processes with non integer dimension (with M. Deaconu) pdf Bernoulli, Vol. 23, no.4B (2017) pp.3744-3771.
• Initial-Boundary Value Problem for the heat equation - A stochastic algorithm (with M. Deaconu) pdf Ann. Appl. Probab. 28 (2018), no. 3, 1943–1976.
  
• Exact simulation of the first-passage time of diffusions (with C. Zucca) pdf
  J. Sci. Comput. 79 (2019), no. 3, 1477–1504.
  
• Exact simulation of first exit times for one-dimensional diffusion processes (with C. Zucca) pdf
  ESAIM Math. Model. Numer. Anal 54 (2020), no.3, 811--844
  
• Exit problem for Ornstein-Uhlenbeck processes: a random walk approach. (with N. Massin) pdf
  Discrete Contin. Dyn. Syst. Ser. B 25 (2020), no. 8, 3199–3215
  
• Approximation of exit times for one-dimensional linear diffusion processes (with N. Massin) pdf
  Comput. Math. Appl. 80 (2020), no. 6, 1668--1682
  
• Exact simulation of diffusion first exit times: algorithm acceleration (with C. Zucca)
  J. Mach. Learn. Res. 23 (2022), 1--19
  
• Strong approximation of Bessel processes (with M. Deaconu) pdf
  Methodol. Comput. Appl. Probab. 25 (2023), no.1, Paper No. 11, 24 pp.
  
• Exact simulation of the first passage time through a given level for jump diffusions (with N. Massin) pdf
  Math. Comput. Simulation 203 (2023), 55--576.
  
• Strong approximation of particular one-dimensional diffusions (with M. Deaconu) pdf
  Discrete Contin. Dyn. Syst. Ser. B 29 (2024), no. 4, pp. 1990-2017.
  

Other research articles

• Stochastic resonance : non-robust and robust tuning notions (avec P. Imkeller et I. Pavlyukevich) pdf
  Probabilistic Problems in Atmospheric and Water Sciences Banach Center Publ.
• Two Mathematical Approaches to Stochastic Resonance (avec P. Imkeller et I. Pavlyukevich) pdf
  Closing volume of the German national research program on interacting stochastic systems of high complexity Springer.
• Stochastic Resonance (avec P. Imkeller) pdf
  Encyclopedia of Mathematical Physics, eds. J.-P. Françoise, G.L. Naber and Tsou S.T. Oxford : Elsevier, 2006.

Book

• Stochastic Resonance: A Mathematical Approach in the Small Noise Limit (avec D. Peithmann, P. Imkeller, I. Pavlyukevich)
  page dédiée
  AMS, 2014, 189 pp., Hardcover, ISBN-10: 1-4704-1049-4, ISBN-13: 978-1-4704-1049-0

Dissertations

• Mémoire de doctorat (juin 2001) Etude de processus de diffusion document pdf
• Mémoire d’habilitation (novembre 2009) Calcul asymptotique lié à l’étude de certains processus stochastiques document pdf

Teaching (2024–2025)

• Algorithmes stochastiques (Master MIGS & PMG)
• TD probabilités (Master MIGS & PMG)
• TD statistique (L2 Psychologie)
• Simulation of stochastic processes (Master in Turin)

Contact

Institut de Mathématiques de Bourgogne, IMB (UMR 5584)
Bureau 302, 9 avenue Alain Savary, BP 47870, 21078 Dijon Cedex
Tél : +33 3 80 39 58 54   
Email : Samuel.Herrmann.at.ube.fr