Pierre Patie
I am broadly interested in the study of non-self-adjoint integro-differential operators arising in the investigation of Markov processes and related objects. This encompasses the following topics:
Interwining relations
Spectral theory
Convergence to equilibrium
First passage time problems
Exponential functional of Lévy processes
Subdiffusive processes
The moment problem
Financial and insurance mathematics
Publications
Click to my
ORCID Profile to see my list of papers
Submitted
Some recently accepted papers
On interweaving relations with L. Miclo Journal of Functional Analysis, 2021
On non-local ergodic Jacobi semigroups: spectral theory, convergence-to-equilibrium and contractivity with P. Cheridito, A. Srapionyan and A. Vaidyanathan Journal de l'Ecole
Polytechnique - Mathématiques, 2021
Risk-neutral pricing techniques and examples with R. A. Jarrow, A. Srapionyan and Y. Zhao Mathematical Finance, 2021
Self-similar Cauchy problems and generalized Mittag-Leffler functions with A. Srapionyan Fractional Calculus and Applied Analysis, 2020
Turàn inequalities and complete monotonicity for a class of entire
functions with C. Bartholmé Analysis Mathematica, 2020
Non-classical Tauberian and Abelian type criteria for the moment problem with A. Vaidyanathan Mathematische Nachrichten, 2020
On Doney's striking factorization of the arc-sine law with L. Alili, C. Bartholmé, L. Chaumont, M. Savov and S. Vakeroudis Special Volume in Honor of Ron Doney, Birkhauser, 2020
Spectral expansions of non-self-adjoint generalized Laguerre semigroups
with M.
Savov
Memoirs of the American Mathematical Society, 2020
Spectral projections correlation structure for short-to-long range dependent processes with A. Srapionyan European Journal of Applied Mathematics, 2020
On some new transformations of Laplace exponents of spectrally negative Lévy processes with M. Chazal and A.E. Kyprianou Special Volume in Honor of Ron Doney, Birkhauser, 2020
On intertwining relations between Ehrenfest, Yule and Ornstein-Uhlenbeck processes with L. Miclo Séminaires de Probabilités, 2020
A spectral approach for hypocoercivity applied to some degenerate hypoelliptic, and non-local operators with with A. Vaidyanathan Kinet. Relat. Mod., 13(3): 479–506, 2020
Analysis of non-reversible Markov chains via similarity orbit with M.C.H. Choi
Combinatorics, Probability and Computing, 29(4), 508-536, 2020
The log-Lévy moment problem via Berg-Urbanik semigroups with A. Vaidyanathan Studia Math., 253, 219-257, 2020
Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups
with M.
Savov and Y. Zhao Ann. Probab., Vol. 47, No. 5, 3231-3277, 2019
Skip-free Markov chains with M.C.H. Choi ,
Trans. Amer. Math. Soc., 371(10), 7301-7342, 2019
Extinction time of non-Markovian self-similar processes, persistence, annihilation of jumps and the Fréchet distribution with R.L. Loeffen and M.
Savov,
J. Stat. Phys., 175(5), 1022-1041, 2019
On a gateway between continuous
and discrete Bessel and Laguerre processes with L. Miclo , Annales Henri Lebesgue 2, 59-98, 2019
Bernstein-gamma functions and exponential functionals of Lévy Processes
with M.
Savov
Electron. J. Probab., 23(75), 101 pp., 2018
Spectral decomposition of fractional operators and a reflected stable semigroup with Y. Zhao
J. Differ. Equations 262(3):1690-1719, 2017
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
Boundary crossing identities for Brownian motion
and some
nonlinear
ode's with L.
Alili
Proc. Amer. Math. Soc. 142, 3811-3824, 2014
Law of the
absorption time of positive self-similar Markov processes
Ann. Probab. ,
40(2): 765-787, 2012
PhD Students
Here are the PhD students I have/had the chance to work with:
Rohan Sarkar (ORIE, Cornell), since 2018
Andrew Chee (ORIE, Cornell), since 2019
Jian Wang (ORIE, Cornell), 2020
Continuous time skip-free Markov process and study of branching process with immigration
Aditya Vaidyanathan (CAM, Cornell), 2019
Contributions to the Stieltjes moment problems and to the intertwining of Markov semigroups
Anna Srapyonian (CAM, Cornell), 2019
Some spectral ideas applied to finance and to self-similar and long-range dependent processes
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