The publications are organized according to the following topics

  1. Books
  2. Monte Carlo methods
  3. Quantization
  4. Discretization of Stochastic Differential Equations
  5. Finance
  6. Optimal transport and longtime behaviour of Markov processes
  7. Molecular simulation
  8. Multiscale models for polymeric fluids
  9. Probabilistic particle methods for PDEs
Books

J.F. Delmas et B. Jourdain, Modèles aléatoires : applications aux sciences de l'ingénieur et du vivant,
collection Mathématiques et Applications, Vol 57, Springer 2006

B. Jourdain, Probabilités et statistique, Ellipses 2009, 2nd edition 2016

Monte Carlo methods

  • R. Flenghi, B. Jourdain, Convergence to the uniform distribution of vectors of partial sums modulo one with a common factor, Preprint arXiv:2308.01874

  • R. Flenghi, B. Jourdain, Central limit theorem for the stratified resampling mechanism, Preprint arXiv:2308.02186

  • A. Alfonsi, J. Corbetta, B. Jourdain, Sampling of one-dimensional probability measures in the convex order and computation of robust option price bounds, International Journal of Theoretical and Applied Finance, 22(3), 2019

  • A. Alfonsi, J. Corbetta, B. Jourdain, Sampling of probability measures in the convex order by Wasserstein projection, Annales de l'Institut Henri Poincaré B, Probabilités et Statistiques, 56(3):1706-1729, 2020

  • G. Fort, B. Jourdain, T. Lelièvre, G. Stoltz, Convergence and efficiency of adaptive importance sampling techniques with partial biasing, Journal of Statistical Physics, 171(2):220-268, 2018

  • R. Assaraf, B. Jourdain, T. Lelièvre, R. Roux, Computation of sensitivities for the invariant measure of a parameter dependent diffusion , Stochastics and Partial Differential Equations: Analysis and Computations 6(2):125-183, 2018

  • G. Fort, B. Jourdain, T. Lelièvre, G. Stoltz, Self-Healing Umbrella Sampling: Convergence and efficiency, Statistics and Computing 27(1):147-168, 2017

  • G. Fort, B. Jourdain, E. Kuhn, T. Lelièvre, G. Stoltz, Convergence of the Wang-Landau algorithm, Mathematics of Computation 84(295), pp 2297-2327, 2015

  • B. Jourdain, T. Lelièvre, B. Miasojedow, Optimal scaling for the transient phase of Metropolis Hastings algorithms: the longtime behavior, Bernoulli 20(4), pp 1930-1978, 2014, DOI: 10.3150/13-BEJ546

  • B. Jourdain, T. Lelièvre, B. Miasojedow, Optimal scaling for the transient phase of the random walk Metropolis algorithm: the mean-field limit, Annals of Applied Probability 25(4), pp 2263-2300, 2015, DOI: 10.1214/14-AAP1048

  • B. Jourdain, B. Lapeyre, P. Sabino, Convenient Multiple Directions of Stratification, International Journal of Theoretical and Applied Finance Vol. 14(6), pp 867–897, 2011, DOI: 10.1142/S0219024911006772

  • P. Etoré, G. Fort, B. Jourdain, E. Moulines, On Adaptive Stratification, Ann. Oper. Res. 189, 127-154, 2011, DOI 10.1007/s10479-009-0638-9

  • P. Etoré, B. Jourdain, Adaptive optimal allocation in stratified sampling methods, Methodology and Computing in Applied Probability 12(3), pp.335-360, 2010.

  • B. Jourdain, Adaptive variance reduction techniques in finance, Advanced Financial Modelling, Radon Series Comp. Appl. Math 8, Ed. by H. Albrecher, W. Runggaldier and W. Schachermayer, de Gruyter, pp. 205-222, 2009.

  • B. Jourdain, J. Lelong, Robust Adaptive Importance Sampling for Normal Random Vectors, Ann. Appl. Probab. 19(5), pp 1687-1718, 2009.

  • J.F. Delmas, B. Jourdain, Does waste-recycling really improve Metropolis-Hastings Monte Carlo algorithm?, Journal of Applied Probability 46(4), pp.938-959, 2009.

  • B. Jourdain, L. Nguyen, Minimisation de l'entropie relative par méthode de Monte-Carlo, C.R.A.S. Série 1, 332, pp.345-350, 2001
    Quantization

  • B. Jourdain, G. Pagès, Quantization and martingale couplings, Latin American Journal of Probability and Mathematical Statistics 19, pp. 1-22, 2022.

  • B. Jourdain, G. Pagès, Optimal dual quantizers of 1D log-concave distributions: uniqueness and Lloyd like algorithm, Journal of Approximation Theory 267, paper n° 105581, 2021.

  • B. Jourdain, G. Pagès, Convex order, quantization and monotone approximations of ARCH models, Journal of Theoretical Probability 35(4):2480-2517, 2022.

    Discretization of Stochastic Differential Equations

  • B. Jourdain, S. Menozzi, Convergence rate of the Euler-Maruyama scheme applied to diffusion processes with Lq-Lp drift coefficient and additive noise, Annals of Applied Probability 33(68), pp. 5382-5412, 2023

  • O. Bencheikh, B. Jourdain, Convergence in total variation of the Euler-Maruyama scheme applied to diffusion processes with measurable drift coefficient and additive noise, SIAM Journal on Numerical Analysis 60(4) pp.1701-1740, 2022

  • B. Jourdain, A. Kebaier, Non-asymptotic error bounds for the Multilevel Monte Carlo Euler method applied to SDEs with constant diffusion coefficient, Electronic Journal of Probability 24(12), pp.1-34, 2019

  • A. Al Gerbi, B. Jourdain, E. Clément, Ninomiya-Victoir scheme : strong convergence properties and discretization of the involved Ordinary Differential Equations, ESAIM: Proceedings and Surveys 59:1-14, 2017

  • A. Al Gerbi, B. Jourdain, E. Clément Asymptotic error distribution for the Ninomiya-Victoir scheme in the commutative case, Preprint ArXiv:1605.08270

  • A. Al Gerbi, B. Jourdain, E. Clément, Asymptotics for the normalized error of the Ninomiya-Victoir scheme, Stochastic Processes and their Applications 128(6):1889-1928, 2018

  • A. Al Gerbi, B. Jourdain, E. Clément, Ninomiya-Victoir scheme: strong convergence, antithetic version and application to multilevel estimators, Monte Carlo Methods and Applications 22(3), 197-228, 2016

  • A. Alfonsi, B. Jourdain, A. Kohatsu-Higa, Optimal transport bounds between the time-marginals of a multidimensional diffusion and its Euler scheme, Electronic Journal of Probability 20, 2015, DOI: 10.1214/EJP.v20-4195

  • A. Alfonsi, B. Jourdain, A. Kohatsu-Higa, Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme, Annals of Applied Probability, Vol 24(3), 1049-1080, 2014

  • B. Jourdain, M. Sbai, Efficient second order weak schemes for stochastic volatility models, Seminar on Stochastic Analysis, Random Fields and Applications VII, Progress in Probability, Vol. 67, pp 395-410, Springer Basel 2013

  • B. Jourdain, M. Sbai, High order discretization schemes for stochastic volatility models, Journal of Computational Finance, 17(2), 2013

  • B. Jourdain, A. Kohatsu-Higa, A review of recent results on approximation of solutions of stochastic differential equations, proceedings of WSAF09, Progress in Probability, Vol. 65, 121-144, 2011.
    Finance

  • B. Jourdain, G. Pagès, Convex ordering of solutions to one-dimensional SDEs, Preprint arXiv:2312.09779

  • H. Andrès, A. Boumezoued, B. Jourdain, Implied volatility (also) is path-dependent, Preprint arXiv:2312.15950

  • B. Jourdain, K. Shao, Non-decreasing martingale couplings, Preprint arXiv:2305.00565

  • B. Jourdain, G. Pammer, An extension of martingale transport and stability in robust finance, Electronic Journal of Probability, 29(57), pp. 1-30, 2024

  • B. Jourdain, G. Pagès, Convex ordering for stochastic Volterra equations and their Euler schemes, accepted in Finance and Stochastics

  • H. Andrès, A. Boumezoued, B. Jourdain, Signature-based validation of real-world economic scenarios, accepted in ASTIN bulletin

  • M. Beiglböck, B. Jourdain, W. Margheriti, G. Pammer, Stability of the Weak Martingale Optimal Transport Problem, Annals of Applied Probability 33(6B), pp. 5382-5412, 2023

  • M. Beiglböck, B. Jourdain, W. Margheriti, G. Pammer, Approximation of martingale couplings on the line in the weak adapted topology, Probability Theory and Related Fields, 183(1-2), 359-413, 2022

  • B. Jourdain, W. Margheriti, A new family of one-dimensional martingale couplings, Electronic Journal of Probability, 25, paper n°136, 1-50, 2020

  • B. Jourdain, A. Zhou, Fake Brownian motion and calibration of a Regime Switching Local Volatility model, Mathematical Finance 30(2), 501-546, 2020

  • B. Jourdain, J. Reygner, Capital distribution and portfolio performance in the mean-field Atlas model, Annals of Finance, 11(2), 151-198, 2015, DOI 10.1007/s10436-014-0258-5

  • G.E. Espinosa, C. Hillairet, B. Jourdain, M. Pontier, Reducing the debt : is it optimal to outsource an investment?, Mathematics and Financial Economics, 10(4), 457-493, 2016, DOI :10.1007/s11579-016-0166-8

  • M. Jeunesse, B. Jourdain, Regularity of the American put option in the Black-Scholes model with general discrete dividends, Stochastic Processes and their Applications, Vol. 112, 3101–3125, 2012, DOI:10.1016/j.spa.2012.05.009

  • B. Jourdain, M. Sbai, Coupling Index and Stocks,Quantitative Finance, Vol. 12(5), 805-818, 2012, DOI: 10.1080/14697681003785959

  • B. Jourdain, M. Vellekoop, Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends, SIAM Journal on Financial Mathematics, Vol. 2, 538-561, 2011, DOI: 10.1137/100800889

  • A. Alfonsi, B. Jourdain, Exact volatility calibration based on a Dupire-type Call-Put duality for perpetual American options, Nonlinear Differential Equations and Applications 16, pp 523-554, 2009.

  • B. Jourdain, A. Zanette, A Moments and Strike Matching Binomial Algorithm for Pricing American Put Options, Decisions in Economics and Finance 31, pp 33-49, 2008.

  • A. Alfonsi, B. Jourdain, General Duality for Perpetual American Options, International Journal of Theoretical and Applied Finance, 11(6), pp. 545-566, 2008.

  • B. Jourdain, M. Sbai, Exact retrospective Monte Carlo computation of arithmetic average Asian options, Monte Carlo Methods and Applications 13(2), pp 135-171, 2007. Erratum in Monte Carlo Methods Appl. 16(2), pp 191-193, 2010.

  • B. Jourdain, Stochastic flows approach to Dupire's formula, Finance and Stochastics 11(4), pp 521-535, 2007.

  • B. Jourdain, Loss of martingality in asset price models with lognormal stochastic volatility, Preprint CERMICS 2004-267 : results previously obtained by C.A. Sin, Complications with stochastic volatility models, Adv. in Appl. Probab. 30 (1998), no. 1, 256--268.

  • B. Jourdain, C. Martini, Approximation of American Put Prices by European Prices via an Embedding Method,
    Annals of Applied Probability, 12(1), pp.196-223, 2002

  • B. Jourdain, C. Martini, American prices embedded in European prices,
    Ann. Inst. Henri Poincaré Anal. nonlinear, 2001, 18(1), pp.1-17

    Optimal transport and longtime behaviour of Markov processes

  • B. Jourdain, K. Shao, Maximal Martingale Wasserstein Inequality, Preprint arXiv:2310.08492

  • B. Jourdain, W. Margheriti, G. Pammer, Lipschitz continuity of the Wasserstein projections in the convex order on the line, Electronic Communications in Probability 28(18), pp. 1-13, 2023

  • R. Flenghi, B. Jourdain, Central limit theorem over non-linear functionals of empirical measures: beyond the iid setting, accepted in Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

  • B. Jourdain, W. Margheriti, One dimensional martingale rearrangement couplings, ESAIM:PS 26, pp. 495-527, 2022

  • O. Bencheikh, B. Jourdain, Approximation rate in Wasserstein distance of probability measures on the real line by deterministic empirical measures, Journal of Approximation Theory 274, paper 105684, 2022

  • B. Jourdain, W. Margheriti, Martingale Wasserstein inequality for probability measures in the convex order, Bernoulli 28(2), pp. 830-858, 2022

  • B. Jourdain, A. Tse, Central limit theorem over non-linear functionals of empirical measures with applications to the mean-field fluctuation of interacting particle systems, Electronic Journal of Probability 26(154), pp1-34, 2021

  • A. Alfonsi, B. Jourdain, Lifted and geometric differentiability of the squared quadratic Wasserstein distance , ESAIM: Probability and Statistics 24, 703-717, 2020

  • A. Alfonsi, J. Corbetta, B. Jourdain, Evolution of the Wasserstein distance between the marginals of two Markov processes , Bernoulli 24(4A), 2461-2498, 2018

  • J. Fontbona, B. Jourdain, On the long time behavior of stochastic vortices systems , Markov Processes and Related Fields 20(4), pp 675-704, 2014

  • A. Alfonsi, B. Jourdain, A remark on the optimal transport between two probability measures sharing the same copula, Statistics and Probability Letters 84, pp 131-134, 2014, DOI 10.1016/j.spl.2013.09.035

  • B. Jourdain, J. Reygner, Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation, Stoch PDE: Anal Comp 1, pp 455-506, 2013, DOI 10.1007/s40072-013-0014-2

  • B. Jourdain, Equivalence of the Poincaré inequality with a transport-chi-square inequality in dimension one, Electronic Communications in Probability 17(43), pp1-12, 2012, DOI: 10.1214/ECP.v17-2115

  • J. Fontbona, B. Jourdain, A trajectorial interpretation of the dissipations of entropy and Fisher information for stochastic differential equations, Annals of Probability 44(1), pp131-170, 2016, DOI: 10.1214/14-AOP969.

  • B. Jourdain, F. Malrieu, Propagation of chaos and Poincaré inequalities for a system of particles interacting through their cdf, Ann. Appl. Probab. 18(5), pp 1706-1736, 2008.

  • B. Jourdain, C. Le Bris, T. Lelièvre, F. Otto, Long-time asymptotics of a multiscale model for polymeric fluid flows, Arch. Rational Mech. Anal., 181, pp 97-148, 2006

    Molecular simulation

  • B. Jourdain, T. Lelièvre, P.-A. Zitt, Convergence of metadynamics: discussion of the adiabatic hypothesis, Annals of Applied Probability, 31(5):2441-2477, 2021

  • G. Fort, B. Jourdain, E. Kuhn, T. Lelièvre, G. Stoltz, Efficiency of the Wang-Landau algorithm: a simple test case, AMRX 2014, pp 275-311, 2014, doi:10.1093/amrx/abu003

  • B. Jourdain, T. Lelièvre, R. Roux, Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process, ESAIM: M2AN 44, pp 831-865, 2010

  • M. El Makrini, B. Jourdain, T. Lelièvre, Diffusion Monte Carlo method: Numerical analysis in a simple case, ESAIM: M2AN 41(2), pp 189-213, 2007

  • E.Cancès, B. Jourdain, T. Lelièvre, Quantum Monte Carlo simulations of fermions. A mathematical analysis of the fixed-node approximation, M3AS, 16(9), pp 1403-1449, 2006

    Multiscale models for polymeric fluids

  • M. Ben Alaya, B. Jourdain, Probabilistic approximation of a nonlinear parabolic equation occuring in rheology, J. Appl. Probab. 44(2), pp 528-546, 2007

  • B. Jourdain, C. Le Bris, T. Lelièvre, Coupling PDEs and SDEs: the Illustrative Example of the Multiscale Simulation of Viscoelastic Flows, in Multiscale Methods in Science and Engineering, B. Engquist, P. L\"otstedt, O. Runborg, eds., Lecture Notes in Computational Science and Engineering 44, Springer, 2005, pp 151-170.

  • B. Jourdain, C. Le Bris, T. Lelièvre, An elementary argument regarding the long-time behaviour of the solution to a stochastic differential equation, Annals of Craiova University, Mathematics and Computer Science series, volume 32, pp 39-47, 2005

  • B. Jourdain, T. Lelièvre, Convergence of a stochastic particle approximation of the stress tensor for the FENE-P model, Preprint CERMICS 2004-263

  • B. Jourdain, T. Lelièvre, C. Le Bris, On a variance reduction technique for the micro-macro simulations of polymeric fluids, J. Non-Newtonian Fluid Mech., 122, pp 91-106, 2004

  • B. Jourdain, T. Lelièvre, C. Le Bris Existence of solution for a micro-macro model of polymeric fluid : the FENE model, Journal of Functional Analysis, 209(1), pp 162-193, 2004

  • B. Jourdain, T. Lelièvre, Mathematical analysis of a stochastic differential equation arising in the micro-macro modelling of polymeric fluids, Probabilistic Methods in Fluids : Proceedings of the Swansea 2002 Workshop, pp 205-223, World Scientific, 2003

  • B. Jourdain, T. Lelièvre, C. Le Bris, Numerical analysis of micro-macro simulations of polymeric fluid flows : a simple case,
    Mathematical Models and Methods in Applied Sciences 12(9),pp.1205-1243, 2002

    Probabilistic particle methods for PDEs

  • B. Jourdain, E. Kahn, Strong solutions to a beta-Wishart particle system, Journal of Theoretical Probability 35(3):1574-1613, 2022

  • O. Bencheikh, B. Jourdain, Weak and strong error analysis for mean-field rank based particle approximations of one dimensional viscous scalar conservation laws, Annals of Applied Probability 32(6):4143-4185, 2022

  • O. Bencheikh, B. Jourdain, Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean, Esaim: ProcS, 65:219-235, 2019

  • N. Fournier, B. Jourdain, Stochastic particle approximation of the Keller-Segel equation and two-dimensional generalization of Bessel processes, Annals of Applied Probability, 27(5):2807-2861, 2017

  • J. Mint Moustapha, B. Jourdain, D. Daucher A probabilistic particle approximation of the "Paveri-Fontana" kinetic model of traffic flow, SMAI Journal of Computational Mathematics, 2:229-253, 2016

  • B. Jourdain, J. Reygner, Optimal convergence rate of the multitype sticky particle approximation of one-dimensional diagonal hyperbolic systems with monotonic initial data, Discrete and Continuous Dynamical System 36(9), pp 4963-4996, 2016, doi:10.3934/dcds.2016015

  • B. Jourdain, J. Reygner, A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data, Journal of Hyperbolic Differential Equations 13(3),pp 441-602, 2016, DOI: 10.1142/S0219891616500144

  • B. Jourdain, J. Reygner, The small noise limit of order-based diffusion processes, Electronic Journal of Probability 19, 2014

  • B. Jourdain, S. Méléard, W. Woyczynski, Lévy Flights in Evolutionary Ecology, Journal of Mathematical Biology 65, pp677-707, 2012, DOI 10.1007/s00285-011-0478-5

  • B. Jourdain, R. Roux, Convergence of a stochastic particle approximation for fractional scalar conservation laws, Stochastic Processes and their Applications 121, pp 957-988, 2011

  • B. Jourdain, S. Méléard, W. Woyczynski, Nonlinear SDEs driven by Lévy processes and related PDEs, Alea 4, pp 1-29, 2008.

  • B. Jourdain, Probabilistic Interpretation via Spatial Derivation of Some Nonlinear Parabolic Evolution Equations, Monte Carlo and Quasi-Monte Carlo Methods 2004, H. Niederreiter and D. Talay (Eds.), Springer-Verlag 2006, pp 197-216

  • B. Jourdain, S. Méléard, W.A. Woyczynski, Probabilistic approximation and inviscid limits for 1-D fractional conservation laws, Bernoulli, 11(4), pp 689-714, 2005

  • B. Jourdain, S. Méléard, W.A. Woyczynski, A probabilistic approach for nonlinear equations involving the fractional Laplacian and a singular operator, Potential Analysis, 23(1), pp 55-81, 2005.

  • B. Jourdain, Uniqueness via probabilistic interpretation for the discrete coagulation fragmentation equation, Communications in Mathematical Sciences, Supplemental issue 1, pp 75-83, 2004

  • B. Jourdain, S. Méléard, Probabilistic interpretation and particle method for vortex equations with Neumann's boundary condition, Proceedings of the Edinburgh mathematical society, 47(3), pp 597-624, 2004

  • E. Debry, B. Sportisse, B. Jourdain, A stochastic approach for the numerical simulation of the general dynamics equation for aerosols,
    Journal of Computational Physics, 184, pp 649-669, 2003

  • B. Jourdain, Nonlinear processes associated with the discrete Smoluchowski coagulation fragmentation equation,
    Markov Processes and Related Fields, 9, pp. 103-130, 2003

  • B. Jourdain, Particules collantes signées et lois de conservation scalaires 1D,
    C.R.A.S. Série 1, 334, pp.233-238, 2002

  • M. Bossy, B. Jourdain, Rate of convergence of a particle method for the solution of a 1D viscous scalar conservation law in a bounded interval,
    Annals of Probability, 30(4), pp.1797-1832, 2002

  • B. Jourdain, Probabilistic characteristics method for a 1D scalar conservation law,
    Annals of Applied Probability, 12(1), pp.334-360, 2002

  • E. Debry, B.Jourdain, B. Sportisse, Modeling aerosol dynamics : a stochastic algorithm,
    APMS 2001, Springer Geosciences 2002, pp. 308-319.

  • M. Bossy, B. Jourdain, A particle method for the solution of a 1D viscous scalar conservation law in a bounded interval ,
    Proceedings of the International Conference on Monte Carlo and Probabilistic Methods for Partial Differential Equations, Monaco 3-5 juillet 2000, Monte Carlo Methods and Applications, 2001, 7(1-2), pp. 45-53

  • B. Jourdain, Probabilistic gradient approximation for a multidimensional viscous scalar conservation law ,
    Stochastics and Stochastics Reports, 2001, 71, pp.243-268

  • B. Jourdain, Probabilistic approximation for a porous medium equation,
    Stochastic Processes and their Applications, 2000, 89(1), pp.81-99

  • B. Jourdain, Diffusion Processes Associated with Nonlinear Evolution Equations for Signed Measures,
    Methodology and Computing in Applied Probability, 2000, 2(1), pp. 69-91

  • B. Jourdain, S. Méléard, Propagation of chaos and fluctuations for a moderate model with smooth initial data,
    Ann. I.H.P. Proba. Stat., 1998, 34/6, p.727-766

  • B. Jourdain, Propagation du chaos trajectorielle pour les lois de conservation scalaire,
    Séminaire de Probabilités XXXII, pp.215-230, Lecture Notes in Mathematics 1686, Springer-Verlag 1998

  • B. Jourdain, Convergence of moderately interacting particle systems to a diffusion-convection equation,
    Stochastic Processes and their Applications, 1998, 73(2), pp.247-270

  • B. Jourdain, Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized Burgers' equations,
    ESAIM : P&S, novembre 1997, vol 1, pp.339-355
    Habilitation à diriger des recherches

    Interprétation probabiliste d'équations d'évolution non linéaires et applications.

    defended on march 20 2002