Pierre Patie
School of Operations Research and Information Engineering
Pierre Patie
Associate Professor
School of Operations Research
and Information Engineering
Cornell University

219 Rhodes Hall
Ithaca, NY 14853
(607) 255-9130 - phone
(607) 255-9129 - fax
pp396 "at" cornell.edu


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Curriculum Vitae
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[Research interests][Events][PhD students] [Papers]

Research interests

  • Spectral theory of non-self-adjoint semigroups

  • Intertwining relationships

  • Convergence to equilibrium for ergodic Markov processes

  • Moment Problem

  • Exit times and additive functionals of discrete and continuous time Markov processes

  • Fine study of Brownian motion, Lévy processes, self-similar processes and some generalizations of the Ornstein-Uhlenbeck process

  • Financial and insurance mathematics


PhD students

  • Anna Srapyonian (CAM, Cornell)

  • Aditya Vaidyanathan (CAM, Cornell)

  • Jian Wang (ORIE, Cornell)

  • Rohan Sarkar (ORIE, Cornell)

  • Michael C.H. Choi (ORIE, Cornell), 2017
    Analysis of non-reversible Markov chains

  • Yixuan Zhao (ORIE, Cornell), 2017
    Spectral expansions and excursion theory for non-self-adjoint Markov semigroups with applications in mathematical finance

  • Christopher Van Weverberg (ULB), co-supervised with G. Deelstra, 2015
    Contributions to the study of affine processes with applications in insurance

  • Carine Bartholmé (ULB), 2014
    Self-similarity and exponential functionals of Lévy processes


  1. Spectral projections correlation structure for short-to-long range dependent processes (with A. Srapionyan ), submitted

  2. Extinction time of non-Markovian self-similar processes, persistence, annihilation of jumps and the Fréchet distribution (with R.L. Loeffen and M. Savov), submitted

  3. Risk-neutral pricing techniques and examples (with R. A. Jarrow, A. Srapionyan and Y. Zhao) , submitted

  4. The log-Lévy moment problem via Berg-Urbanik semigroups (with A. Vaidyanathan), submitted

  5. Non-classical Tauberian and Abelian type criteria for the moment problem (with A. Vaidyanathan), submitted

  6. Analysis of non-reversible Markov chains via similarity orbit (with M.C.H. Choi), submitted

  7. Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups (with M. Savov and with Y. Zhao), submitted

  8. Absolute ruin in the Ornstein-Uhlenbeck type risk model (with R.L. Loeffen), submitted

  9. Skip-free Markov chains (with M.C.H. Choi),
    Trans. Am. Math. Soc., accepted, 41p., 2018

  10. On a gateway between continuous and discrete Bessel and Laguerre processes (with L. Miclo),
    Annales Henri Lebesgue, accepted, 41p., 2018

  11. Spectral expansions of non-self-adjoint generalized Laguerre semigroups (with M. Savov )
    Mem. Amer. Math. Soc., accepted, 179pp., 2018

  12. Bernstein-gamma functions and exponential functionals of Lévy Processes (with M. Savov )
    Electron. J. Probab., 23(75), 101 pp., 2018

  13. Option pricing in a one-dimensional affine term structure model via spectral representations (with M. Chazal, and R.L. Loeffen)
    SIAM Journal on Financial Mathematics, 9(2), 634-664, 2018

  14. Purely excessive functions and hitting times of continuous-time branching processes (with F. Avram and with J. Wang)
    Methodol. Comput. Appl. Probab., online, 2018

  15. Smoothness of continuous state branching with immigration semigroups (with M. Chazal and R.L. Loeffen)
    J. Math. Anal. Appl. 459(2):619-660, 2018

  16. Spectral decomposition of fractional operators and a reflected stable semigroup (with Y. Zhao)
    J. Differ. Equations 262(3):1690-1719, 2017

  17. Cauchy problem of the non-self-adjoint Gauss-Laguerre semigroups and uniform bounds of generalized Laguerre polynomials (with M. Savov )
    J. Spectr. Theory 7:797-846, 2017

  18. Sufficient conditions for continuous time finite skip-free Markov chains to have real eigenvalues (with M.C.H. Choi)
    Math. and Comp. Appr. Adv. Modern Scienc. and Engin., 529--536, 2016

  19. Convergence analysis of spectral expansion of stable related semigroups (with Y. Zhao)
    Math. and Comp. Appr. Adv. Modern Scienc. and Engin., 787--797, 2016

  20. Boundary crossing identities for Brownian motion and some nonlinear ode's (with L. Alili)
    Proc. Amer. Math. Soc. 142, 3811-3824, 2014

  21. A transformation for Lévy processes with one-sided jumps with applications (with M. Chazal and A.E. Kyprianou)
    Adv. Appl. Prob., to appear, 2014

  22. Exponential functionals of Lévy processes: generalized Weierstrass products and Wiener-Hopf factorization (with M. Savov )
    C. R. Math. Acad. Sci. Paris, 351, no. 9-10, 393-396, 2013

  23. Asion options under one-sided  Lévy models
    J. of Appl. Prob. 50(2), 359-373, 2013

  24. Extended factorizations of exponential functionals of Lévy processes, (with M. Savov )
    Electron. J. Probab., 17(38): 1-22, 2012

  25. Law of the absorption time of positive self-similar Markov processes
    Ann. Probab., 40(2): 765-787, 2012

  26. A Wiener-Hopf type factorization for the exponential functional of Lévy processes (with J.-C. Pardo and M. Savov )
    J. London Math. Soc., 86(3): 930-956, 2012

  27. Optimal stopping problems for some Markov processes (with M. Cissé and E. Tanré)
    Ann. Appl. Probab., 22(3): 1243–1265, 2012

  28. Intertwining certain fractional operators (with T. Simon)
    Potent. Anal., 36: 569-587, 2012

  29. A Ciesielski-Taylor type identity for positive self-similar Markov processes (with A.E. Kyprianou)
    Ann. Inst. H. Poincaré Probab. Statist., 47(3):917–928, 2011

  30. A refined factorization of the exponential law
    Bernoulli, 17(2):814-826, 2011

  31. Boundary crossing identities for diffusions having the time inversion property (with L. Alili)
    J. Theoret. Probab., (23): 65–84, 2010

  32. Exponential functional of a new family of Lévy processes and self-similar continuous state branching processes with immigration
    Bull. Sci. Math., 133(4):355-382, 2009

  33. Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes
    Ann. Inst. H. Poincaré Probab. Statist., 45 (3):667--684, 2009

  34. Law of the exponential functional of one-sided Lévy processes and Asian options
    C. R. Acad. Sci. Paris, Ser. I ,347:407–411, 2009

  35. A few remarks on the supremum of stable processes
    Statist. Probab. Lett., 79:1125--1128, 2009

  36. q-invariant functions for some generalizations of the Ornstein-Uhlenbeck semigroup
    ALEA Lat. Am. J. Probab. Math. Stat.,4:31--43, 2008

  37. First exit time probabilities for multidimensional diffusion: A PDE-based approach (with C. Winter)
    J. Comput. Appl. Math., 222(1):43--53, 2008

  38. On the joint law of the L1 and L2 norms of a 3-dimensional Bessel bridge (with L. Alili)
    Séminaire de Probabilités XL:247-264, Lecture Notes in Math., 1899, Springer, Berlin, 2007

  39. Two-sided exit problem for a spectrally negative α-stable Ornstein-Uhlenbeck process and the Wright's generalized hypergeometric functions
    Elect. Com. Prob.,12:146-160, 2007

  40. Strategic Long-Term Financial Risks: The one dimensional case (with P. Embrechts   and R. Kaufmann)
    Comput. Optim. Appl., 32(1-2):61-90,2005

  41. Representations of the first hitting time density of an Ornstein-Uhlenbeck process (with L. Alili  and J.L. Pedersen )
    Stochastic Models, 21(4):967-980, 2005

  42. On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance
    Stochastic Process. Appl., 115(4):593-607, 2005

  43. Sur les premiers instants de croissement du mouvement brownien et d'une famille de courbes continues (with L. Alili)
    C. R. Acad. Sci. Paris Sér. I Math., 340(3):225-228, 2005

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