Research themes Isospectral classes Spectral theory Hypocoercivity via spectral methods First passage time problems Computational Mathematics Exponential functional of Lévy processes Subdiffusive processes The moment problem Financial and insurance mathematics ☰ Pierre Patie Pierre Patie Isospectral classes Novel visions in the theory of self-adjoint operators through the lens of algebras Weak similarity orbit of (log)-self-similar semigroups in the Euclidean space with R. Sarkar, Proceedings of the London Mathematical Society, 2023 Discrete self-similar and ergodic Markov chains with L. Miclo and R. Sarkar, Annals of Probability, 2023 On interweaving relations with L. Miclo J. Funct. Anal. 280 (2021), no. 3, Paper No. 108816, 53 pp. On non-local ergodic Jacobi semigroups: spectral theory, convergence-to-equilibrium and contractivity with P. Cheridito, A. Srapionyan, A. Vaidyanathan, 2019 Risk-neutral pricing techniques and examples with R. A. Jarrow, A. Srapionyan and Y. Zhao, 2019 Analysis of non-reversible Markov chains via similarity orbit with M.C.H. Choi, Combinatorics, Probability and Computing, 29p., 2019, A spectral approach for hypocoercivity applied to some degenerate hypoelliptic, and non-local operators with A. Vaidyanathan, Kinet. Relat. Mod., 2019 On intertwining relations between Ehrenfest, Yule and Ornstein-Uhlenbeck processes with L. Miclo, Sém. Prob. LNM, 21p., 2019 Spectral expansions of non-self-adjoint generalized Laguerre semigroups with M. Savov, Mem. Amer. Math. Soc. 179p., 2019 On a gateway between continuous and discrete Bessel and Laguerre processes with L. Miclo, Annales Henri Lebesgue, 2, 59-98, 2019 Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups with M. Savov and with Y. Zhao, Ann. Probab. , 47, No. 5, 3231-3277, 2019 Skip-free Markov chains with M.C.H. Choi, Trans. Amer. Math. Soc., 371(10), 7301-7342, 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 Intertwining certain fractional operators, with T. Simon Potent. Anal., 36: 569-587, 2012 Spectral theory Novel visions in the theory of self-adjoint operators through the lens of algebras Weak similarity orbit of (log)-self-similar semigroups in the Euclidean space with R. Sarkar, Proceedings of the London Mathematical Society, 2023 Discrete self-similar and ergodic Markov chains with L. Miclo and R. Sarkar, Annals of Probability, 2022 On interweaving relations with L. Miclo, Journal of Functional Analysis, 280 (2021), no. 3, Paper No. 108816, 53 pp. On non-local ergodic Jacobi semigroups: spectral theory, convergence-to-equilibrium and contractivity with P. Cheridito, A. Srapionyan, A. Vaidyanathan, 2019 A spectral approach for hypocoercivity applied to some degenerate hypoelliptic, and non-local operators with A. Vaidyanathan, Kinet. Relat. Mod., 2019 Self-similar Cauchy problems and generalized Mittag-Leffler functions with A. Srapionyan, 2019 Spectral projections correlation structure for short-to-long range dependent processes with A. Srapionyan, 2019 Analysis of non-reversible Markov chains via similarity orbit with M.C.H. Choi, 2019, Spectral expansions of non-self-adjoint generalized Laguerre semigroups, 2019 with M. Savov, Mem. Amer. Math. Soc. 179p., 2019 Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups with M. Savov and with Y. Zhao, Ann. Probab. , 47, No. 5, 3231-3277, 2019 Skip-free Markov chains with M.C.H. Choi, Trans. Amer. Math. Soc., 371(10), 7301-7342, 2019 Smoothness of continuous state branching with immigration semigroups with M. Chazal and R.L. Loeffen J. Math. Anal. Appl. 459(2):619-660, 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 Hypocoercivity via spectral methods Discrete self-similar and ergodic Markov chains with L. Miclo and R. Sarkar, Annals of Probability, 2023 On interweaving relations with L. Miclo, Journal of Functional Analysis, 280 (2021), no. 3, Paper No. 108816, 53 pp. A spectral approach for hypocoercivity applied to some degenerate hypoelliptic, and non-local operators with A. Vaidyanathan, Kinet. Relat. Mod., 2019 On non-local ergodic Jacobi semigroups: spectral theory, convergence-to-equilibrium and contractivity with P. Cheridito, A. Srapionyan, A. Vaidyanathan, 2019 Analysis of non-reversible Markov chains via similarity orbit with M.C.H. Choi, 2019, Spectral expansions of non-self-adjoint generalized Laguerre semigroups, 2019 with M. Savov, Mem. Amer. Math. Soc. 179p., 2019 Skip-free Markov chains with M.C.H. Choi, 2019 Trans. Amer. Math. Soc., 371(10), 7301-7342, 2019 First passage time problems Non-local heat equation with moving boundary and curve-crossing of delayed Brownian motion with G. Ascione and B. Toaldo Fluctuation theory of continuous-time skip-free downward Markov chains with applications to branching processes with immigration with R.L. Loeffen and J. Wang Jacobi processes with jumps as neuronal models: a first passage time analysis with G. D'Onofrio and L. Sacerdote First passage times over stochastic boundaries for subdiffusive processes with C. Constantinescu and R.L. Loeffen, 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), pp 1022–1041, 2019 Skip-free Markov chains with M.C.H. Choi, Trans. Amer. Math. Soc., 371(10), 7301-7342, 2019 Purely excessive functions and hitting times of continuous-time branching processes with F. Avram and with J. Wang, Methodol. Comput. Appl. Probab., 21:391-399, 2019 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 Optimal stopping problems for some Markov processes, with M. Cissé and E. Tanré, Ann. Appl. Probab., 22(3): 1243–1265, 2012 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 Boundary crossing identities for diffusions having the time inversion property, with L. Alili, J. Theoret. Probab., (23): 65–84, 2010 Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes, Ann. Inst. H. Poincaré Prob.. Stat., 45 (3):667--684, 2009 A few remarks on the supremum of stable processes Statist. Probab. Lett., 79:1125--1128, 2009 q-invariant functions for some generalizations of the Ornstein-Uhlenbeck semigroup, ALEA Lat. Am. J. Probab. Math. Stat.,4:31--43, 2008 First exit time probabilities for multidimensional diffusion: A PDE-based approach, with C. Winter) J. Comput. Appl. Math., 222(1):43--53, 2008 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 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 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 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 Computational mathematics Isospectral schemes for exact algorithms for stochastic processes and PDE's with A. Chee, X.Y. Han, Y. Liu, R. Sarkar and T. Tian Risk-neutral pricing techniques and examples with R. A. Jarrow, A. Srapionyan and Y. Zhao, 2021 Option pricing in a one-dimensional affine term structure model via spectral representations with M. Chazal, and R.L. Loeffen SIAM J Financ. Math., 9(2), 634-664, 2018 First exit time probabilities for multidimensional diffusion: A PDE-based approach, with C. Winter Journal of Computational and Applied Mathematics, 2008 Strategic Long-Term Financial Risks: The one dimensional case, with P. Embrechts and R. Kaufmann Comput. Optim. Appl., 32(1-2):61-90, 2005 Risk Management for Derivatives in Illiquid Markets: A Simulation Study, with R. Frey, Advances in Finance and Stochastics, 137--159, Springer, Berlin, 2002 Exponential functional of Lévy processes On Doney's striking factorization of the arc-sine law with L. Alili, C. Bartholmé, L. Chaumont, M. Savov and S. Vakeroudis, 2019 Spectral expansions of non-self-adjoint generalized Laguerre semigroups with M. Savov, Mem. Amer. Math. Soc. 179p., 2019 Bernstein-gamma functions and exponential functionals of Lévy Processes with M. Savov, Electron. J. Probab., 2018 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 Law of the absorption time of positive self-similar Markov processes, Ann. Probab., 40(2): 765-787, 2012 Extended factorizations of exponential functionals of Lévy processes, with M. Savov Electron. J. Probab., 17(38): 1-22, 2012 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 A refined factorization of the exponential law Bernoulli, 17(2):814-826, 2011 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 Law of the exponential functional of one-sided Lévy processes and Asian options, C. R. Acad. Sci. Paris, Ser. I ,347:407–411, 2009 Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes, Ann. Inst. H. Poincaré Prob.. Stat., 45 (3):667--684, 2009 Subdiffusive processes Non-local heat equation with moving boundary and curve-crossing of delayed Brownian motion with G. Ascione and B. Toaldo First passage times over stochastic boundaries for subdiffusive processes with C. Constantinescu and R.L. Loeffen, 2019 Self-similar Cauchy problems and generalized Mittag-Leffler functions with A. Srapionyan, 2019 First passage times over stochastic boundaries for subdiffusive processes with C. Constantinescu and R.L. Loeffen, 2019 Spectral projections correlation structure for short-to-long range dependent processes with A. Srapionyan, 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), pp 1022–1041, 2019 The moment problem Non-classical Tauberian and Abelian type criteria for the moment problem with A. Vaidyanathan, 2019 The log-Lévy moment problem via Berg-Urbanik semigroups with A. Vaidyanathan, Studia Math., 26p., 2019 Financial and insurance mathematics First passage times over stochastic boundaries for subdiffusive processes with C. Constantinescu and R.L. Loeffen, 2022 Risk-neutral pricing techniques and examples with R. A. Jarrow, A. Srapionyan and Y. Zhao, 2021 Option pricing in a one-dimensional affine term structure model via spectral representations with M. Chazal, and R.L. Loeffen SIAM J Financ. Math., 9(2), 634-664, 2018 Asion options under one-sided Lévy models J. of Appl. Prob. 50(2), 359-373, 2013 Law of the exponential functional of one-sided Lévy processes and Asian options, C. R. Acad. Sci. Paris, Ser. I ,347:407–411, 2009 Strategic Long-Term Financial Risks: The one dimensional case, with P. Embrechts and R. Kaufmann Comput. Optim. Appl., 32(1-2):61-90, 2005 On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance Stochastic Process. Appl., 115(4):593-607, 2005 Risk Management for Derivatives in Illiquid Markets: A Simulation Study, with R. Frey, Advances in Finance and Stochastics, 137--159, Springer, Berlin, 2002