What each probabilist should have read

DEA DE PROBABILITÉS de l' UNIVERSITÉ de PARIS VI (98-99)

• Applied Probability Program

  • Probability
    • P. Billingsley : Probability and Measure. Wiley (Second edition, 1987).
    • N. Bouleau : Processus stochastiques et applications. Hermann 1988.
    • L. Breiman : Probability and Stochastic Processes.
    • R. Durrett : Brownian motion and martingales in analysis. Wadsworth (1984).
    • A. Shiryaev : Probability Theory.
  • Simulations et Méthodes de Monte-Carlo
    • Hua Loo Keng, Wang Yuan : Application of number theory to numerical analysis. Springer 1981.
    • L. Devroye : Non uniform random variable generation. Springer 1986.
    • N. Bouleau et D. Talay : Probabilités numériques. INRIA.
    • N. Bouleau et D. Lépingle : Numerical methods for stochastic processes. Wiley 1994.
  • Introduction aux processus stochastiques
    • A. Shiryaev : Probability Theory.
    • L. Breiman : Probability and Stochastic Processes.
    • K.L. Chung, R. Williams : Introduction to stochastic integration. Birkhaüser.
    • N. Bouleau : Processus stochastiques et applications. Hermann 1988.
    • B. Oksendal : Stochastic Differential Equations. Springer.
    • I. Karatzas, S. Shreve : Brownian motion and Stochastic calculus. Springer.
    • R. Durrett : Brownian motion and martingales in analysis. Wadsworth (1984).
  • Algorithmes stochastiques
    • J. Neveu : Martingales à temps discret. Masson.
    • A. Benvéniste, M. Métivier, P. Priouret : Algorithmes adaptatifs et approximation stochastiques. Masson, Paris, 1987.
    • H.J. Kushner, D.S. Clark : Stochastic Approximation for Constrained and Unconstrained Systems. Applied Math. Science Series, 26, Springer, 1978, 261p.
    • M. Duflo : Algorithmes stochastiques. Springer, Coll. Mathématiques et applications, 23, 1996.
  • Théorèmes limites pour l'étude des files d'attente
    • S. Asmussen : Applied Probability and Queues. John Wiley and Sons Ltd, 1987.
    • A. Barbour , L. Holst and S. Janson : Poisson approximation. Oxford science publications, 1992.
    • A. Dembo and 0. Zeitouni : Large deviations techniques and applications. Jones and Bartlett, 1983.

• Financial Mathematics Program

  • Analyse financière et Processus stochastiques
    • M. Musiela - M. Rutkowski : Martingales Methods in Financial Modelling. Springer.
    • T.E. Copeland and J.F. Weston : Financial theory and corporate-policy, (Addison-Wesley).
    • J. Cox et M. Rubinstein : Options Market. (1985).
    • R.A. Dana et M. Jeanblanc-Piqué : Marchés financiers en temps continu. Economica (1994).
    • G. Demange et J.C. Rochet : Méthodes mathématiques de la Finance. Economica (1992).
    • D. Duffie : Dynamic Asset Pricing. Princeton (1993).
    • I. Karatzas and Shreve : Brownian motion and stochastic calculus. Springer (1987).
    • D. Lamberton - B. Lapeyre : Introduction au calcul stochastique appliqué à la Finance. Ellipse (1991) .
    • A.G. Malliaris and W.A. Brock : Stochastic Methods in Economica and Finance. North Holland, (1991).
    • R. Dixit et Pindyck : Investment under uncertainty. Princeton (1994).
  • Assurances
    • H. Niederreiter (1992) : Random generator and quasi-Monte Carlo methods.
    • N. Newton (1994) : Variance reduction methods for diffusion process.
    • E. Fournié, J.M. Lasry, P.L. Lions (1997) : Nonlinear methods in Finance.
    • E. Fournié, J.M. Lasry, P.L. Lions, N. Touzi, T. Lebuchoux (1998) : Application of Mallilavin calculus in Finance.
    • W.H. Press and al. (1992) : Numerical recepies.
    • B. Lapeyre, E. Pardoux (1998) : Methodes de Monte Carlo pour les équations de transport et les diffusions.
    • R. Dautray (1989) : Méthodes probabilistes pour les équations de la physique.
  • Théorie financière
    • Brealey and Myers : Principles of Corporate Finance.
    • Ferrandier et V. Koen : Marchés de capitaux et techniques financières. Economica.
    • Kenneth Garbade : Securities Markets. Mac Graw-Hill.
    • Copeland et Weston : Financial Theory and Corporate policy.
    • Lessard : International Financial Management.
    • Merton : Continuous Time Finance.
  • Modélisation linéaire et non linéaire des séries temporelles
    • A. Banerjee, J. Doleado, J. Galbraith and D. Hendry, 1993 : Co-integration, Error-correction, and the econometric analysis of non-stationary data. Oxford University Press.
    • P. Brockwell and Davis, 1991 : Time series : theory and methods. Second edition. Springer-Verlag.
    • W. Fuller, 1996 : Introduction to statistical time series. Second edition, Wiley.
    • C. Gourieroux, 1997 : ARCH models and financial applications. Springer-Verlag.
    • C.W.J. Granger and T. Teräsvirta, 1993 : Modelling nonlinear economic relationships. Oxford University Press.
    • J. Hamilton, 1994 : Time series analysis. Princeton University Press.
    • T.C. Mills, 1993 : The econometric modelling of financial time series. Cambridge University Press.
    • G. Reinsel, 1997 : Elements of multivariate time series analysis. Second edition, Springer.
    • N. Tong, 1990 : Non linear time series - A dynamic system approach. Clarendon Press Oxford.
  • Futures et options
    • C. Chazot et P. Claude, 1994 : Les swaps, concepts et applications. Economica.
    • S. Hayat, P. Poncet et R. Portait, 1993 : Mathématiques financières, évaluation des actifs et analyse du risque. Dalloz.
    • J. Hull,1993 : Options, futures and forwards. Prentice Hall International Editions.
    • R.A. Dana et M. Jeanblanc Picqué, 1994 : Marchés financiers en temps continu, valorisation et équilibre. Economica.
  • Modèles financiers Méthodes numériques et Statistiques
    • D.P.Bertsekas : Dynamic Programming : Deterministic and Stochastic Models. Prentice-Hall, Englewood Cliffs, N.J., 1987.
    • H.J. Kushner : Probability Methods for Approximations in Stochastic Control and for Elliptic Equations. Academic Press, New-York, 1977.
    • D. Lamberton and B. Lapeyre : Une Introduction au Calcul Stochastique Appliquée à la Finance. Editions Eyrolles, 1997.
    • H. Niederreiter : Random Number Generation and Quasi-Monte-Carlo Methods. CBMS-NSF Regional Conference Series in Appl. Math. SIAM, 1992.
    • P.A. Raviart and J.M. Thomas : Introduction à l'analyse numérique des équations aux dérivées partielles. Masson, Paris, 1983.
    • B.D. Ripley : Stochastic Simulation. Wiley 1987.
    • D. Talay : Simulation and numerical analysis of stochastic differential systems : a review. In P. Krée and W. Wedig, editors, Probabilistic Methods in Applied Physics, volume 451 of Lecture Notes in Physics, chapter 3, pages 54-96. Springer-Verlag, 1995.
    • B. Lapeyre, A. Sulem et D. Talay : Understanding Numerical Analysis for Option Pricing. En préparation, Cambridge University Press.
  • Introduction aux processus stochastiques
    • A. Shiryaev : Probability Theory.
    • L. Breiman : Probability and Stochastic Processes.
    • K.L. Chung, R. Williams : Introduction to stochastic integration. Birkhaüser.
    • N. Bouleau : Processus stochastiques et applications. Hermann 1988.
    • B. Oksendal : Stochastic Differential Equations. Springer.
    • I. Karatzas, S. Shreve : Brownian motion and Stochastic calculus. Springer.
    • R. Durrett : Brownian motion and martingales in analysis. Wadsworth (1984).

• Stochastic Processes Program

  • J. BERTOIN : Mouvement brownien et calcul stochastique.
    • K.L. Chung, R.J. Williams : Introduction to stochastic integration. Birkhauser (1990).
    • C. Dellacherie et P.A. Meyer : Probabilités et Potentiels, Vol. II, Théorie des Martingales. Hermann. (1980).
    • R. Durrett : Brownian motion and martingales in analysis. Wadsworth (1984).
    • N. Ikeda, S. Watanabe : Stochastic differential equations and diffusion processes. North Holland (Second edition, 1988).
    • D. Revuz, M. Yor : Continuous martingales and Brownian motion. Springer (1991).
    • D.W. Stroock, S.R.S. Varadhan : Multidimensional diffusion processes. Springer (1979).
    • I. Karatzas, S. Shreve : Brownian motion and stochastic calculus. Springer (1987).
    • L.C.G. Rogers, D. Williams : Diffusions, Markov Processes and Martingales. Wiley (1987).
  • Markov processes (Jacod)
    (no references given)
  • S. MELEARD - C. DONATI : Martingales et théorèmes limites.
    • Neveu : Martingales à temps discret. Masson (1972)
    • Billingsley : Convergence of probability measures. Wiley (1969).
    • Parthasarathy : Probability measures on metric spaces. Academic Press (1967).
    • Jacod et Shiryaev : Limit theorems for stochastic processes. Springer (1987).
    • Ethier et Kurtz : Markov processes. Characterization and convergence. Wiley (1986).
  • Modèles probabilistes et systèmes dynamiques.
    • R. Bowen : Equililibrium states and the ergodic theory of Anosov diffeomorphisms, Lectures Notes in Math. 470, Springer Verlag, (1975)
    • S. Lalley : Probabilistic methods in certain counting problems in ergodic theory. In: Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Bedford, Keane, Series Ed. , Oxford University Press (1991)
    • W. Parry : Topics in Ergodic Theory. Cambridge University Press, 75, (1981)
    • W. Parry & M. Pollicott :Zeta Functions and the periodic orbit structure of hyperbolic dynamics. Astérisque 187-188, Soc. Math. France (1990)
    • Ya. G. Sinai :Introduction to Ergodic Theory. Princeton University Press (1976) P. Walters :An introduction to Ergodic Theory. Graduate Textes in Maths 79, Springer-Verlag.
  • C. LANDIM - S. OLLA : Limite hydrodynamique de systèmes de particules.
    • M.D. Donsker and S.R.S. Varadhan (1989) : Large deviations from hydrodynamic scaling limit. Comm. Pure Appl. Math 42 243-270.
    • M.Z. Guo, G.C. Papanicolaou and S.R.S. Varadhan (1988) : Nonlinear diffusion limit for a system with nearest neighbor interactions. Comm. Math. Phys. 118 31-59.
    • C. Kipnis and C. Landim (1995) : Hydrodynamical Limit of Interacting Particle Systems. Preprint.
    • C. Kipnis, S. Olla, S.R.S. Varadhan (1989) : Hydrodynamics and large deviations for simple exclusion processes. Comm. Pure Appl. Math., 42, 115-137.
    • C. Kipnis, S.R.S. Varadhan : Central limit theorem for additive functionals of reversible Markov process and applications to simple exclusions. Comm. Math. Phys. 104, 1-19 (1986).
    • C. Landim (1993) : Conservation of local equilibrium for asymmetric attractive particle systems on . Ann. Prob. 21 1782-1808.
    • T.M Liggett (1985) : Interacting Particle Systems. Springer-Verlag, New York.
    • S. Olla : Lectures on Homogenization of Diffusion Processes in Random Fields. Publications de l'Ecole Doctorale de l'Ecole Polytechnique, (1994).
    • S. Olla, S.R.S. Varadhan et H.T. Yau : Hydrodynamic Limit for a Hamiltonian System with Weak Noise. Comm. Math. Phys. 155, 523-560 (1993).
    • F. Rezakhanlou : Hydrodynamic limit for attractive particle systems on . Comm.Math.Phys. 140 417-448, (1990).
    • H. Spohn : Large Scale Dynamics of Interacting Particles, Springer-Verlag New York (1991).
    • H.T. Yau : Relative entropy and hydrodynamics of Ginsburg-Landau models. Lett. Math. Phys., 22, 63-80, (1991).
  • A. MILLET : Grandes déviations et applications.
    • R. Azencott : Grandes déviations et applications. Ecole d'Eté de Probabilités de Saint-Flour 1978. Lecture Notes in Math. 774, 1980.
    • A. Dembo, O. Zeitouni : Large Deviations Techniques and Applications. Jones and Barlett Publishers, 1993.
    • J.D. Deuschel, D.W. Stroock : Large Deviations. Academic Press Inc., 1989.
    • S.R.S. Varadhan : Large Deviations. Ecole d'Eté de Probabilités de Saint-Flour 1985-87. Lecture Notes in Math. 1362, 1988.
  • A. TSYBAKOV : Estimation fonctionnelle.
    • A.P. Korostelev, A.B Tsybakov : Minimax theory of image reconstruction. Springer, N.Y. e.a., Lecture Notes in Statist. v. 82, 1993.
    • I.A.Ibragimov, R.Z. Hasminskii : Statistical estimation: asymptotic theory. Springer, N.Y. e.a., 1981.
  • M. Yor: Etude approfondie du mouvement brownien
    • I. Karatzas - S. Shreve : Brownian motion and stochastic calculus. Springer (1987).
    • J.F. Le Gall : Some properties of planar Brownian motion. In : Ecole d'Eté de Probabilités de Saint-Flour XX, 1990. Lecture Notes in Mathematics 1527. Springer (1992).
    • D. Revuz - M. Yor : Continuous martingales and Brownian motion. Springer-Verlag, (1991).
    • L.C.G. Rogers - D. Williams : Diffusions, Markov Processes and Martingales. Wiley (1987).