Juan Carlos Pardo Millán

Research Interests:

• Path decomposition of Markov processes.
• Lévy processes and random walks.
• Self-similar Markov processes and self-similar additive processes
• Branching processes, fragmentation processes and random trees.
• Optimal stopping problems and stochastic games.
• Stochastic analysis.

Papers and preprints:

• Occupation times of refracted Lévy processes. (with A.E. Kyprianou. and J.L. Pérez.)
  Arxiv: 1205.0756. (2012).
• Hitting distributions of alpha-stable processes via path censoring and self-similarity. (with A.E. Kyprianou. and A. Watson.)
  Arxiv: 1112.3690. (2011).
• Fluctuations of stable processes and exponential functionals of hypergeometric Lévy processes. (with A. Kuznetsov )
  To appear in Acta Applicandae Mathematicae (2012).
• A Wiener-Hopf type factorization for the exponential functional of Lévy processes. (with P. Patie and M. Savov.)
  To appear in the Journal of the London Mathematical Society (2012).
• On the density of exponential functional of Lévy processes. (with V.M. Rivero and K. van Schaik.)
  To appear in Bernoulli (2012).
• Meromorphic Lévy processes and their fluctuation identities. (with A. Kuznetsov and A.E. Kyprianou. )
  To appear in the Annals of Applied Probability (2012).
• An optimal stopping problem for fragmentation processes. (with A.E. Kyprianou.)
  Stochastic Process. Appl. Vol 122, (2012), No. 4, 1210--1225.
• Fluctuation theory and exit systems for positive self-similar Markov processes. (with L. Chaumont , A.E. Kyprianou and V.M. Rivero.)
  Ann. Probab., (2012), 40, 245--279.
• Distributional properties of exponential functional of Lévy processes. (with A. Kuznetsov and M. Savov.)
  Electron. J. Probab. Vol. 17, (2012), No. 8, 1--35.
• A Wiener-Hopf Monte Carlo simulation technique for Lévy processes. (with A. Kuznetsov, A.E. Kyprianou and K. van Schaik. )
  Ann. Appl. Probab. 21 (2011), 6, 2171--2190.
• The Gapeev-Kühn stochastic game driven by a spectrally positive Lévy processes. (with E. Baurdoux and A.E. Kyprianou.)
  Stochastic Process. Appl. Vol 121, (2011), No. 6, 1266--1289.
• Explicit identities for Lévy processes associated to symmetric stable processes. (with M.E. Caballero and J.L. Pérez.)
  Bernoulli 17 (2011), 1, 34--59.
• Exact and asymptotic n-tuple laws at first and last passage. (with A.E. Kyprianou and V.M. Rivero.)
  Ann. of Appl. Probab. 20 (2010), 2, 522--564.
• On Lamperti stable processes. (with M.E. Caballero and J.L. Pérez.)
  Probab. Math. Statist. Vol 30, (2010), 1--28.
• On the genealogy of conditioned stable Lévy forests. (with L. Chaumont.)
  ALEA Lat. Am. J. of Probab. Math. Stat., (2009), 6, 261--279.
• The upper envelope of positive self-similar Markov processes.
  J. Theor. Probab. Vol. 22, (2009), No. 2, 514--542.
• Some explicit identities associated with positive self-similar Markov processes. (with L. Chaumont and A.E. Kyprianou.)
  Stochastic Process. Appl. Vol 119, (2009), No. 3, 980--1000.
• Continuous state branching processes and self-similarity. (with A.E. Kyprianou.)
  J. Appl. Probab. Vol 45, (2008), No. 4, 1140--1160.
• On the rate of growth of Lévy processes with no positive jumps conditioned to stay positive.
  Elect. Comm. in Probab. Vol. 13, (2008), No. 47, 494--506.
• On the future infimum of positive self-similar Markov processes.
  Stochastics 78, (2006), No. 3, 123--155.
• The lower envelope of positive self-similar Markov processes. (with L. Chaumont.)
  Electron. J. Probab. Vol. 11, (2006), No. 49, 1321--1341.

Theses:

• Asymptotic behaviour of positive self-similar Markov processes and conditioned stable Lévy forests. (2007)
  PHD thesis at University of Paris VI, under the supervision of Loïc Chaumont.
• Relación entre los procesos de ramificación y los procesos de Lévy. (2000)
  Tesis de Licenciatura at Instituto de Matemáticas, UNAM, under the supervision of María Emilia Caballero.

Links:

• CIMAT
• Probability Laboratory at Bath
• Laboratoire de Probabilités et Modèles Aléatoires.
• Instituto de Matemáticas, UNAM
• Probability Web.

Teaching and some additional material:

• El proceso de ramificación continua. (The continuous state branching process).
• Martingalas y tiempos de paro en tiempo continuo. (Martingales and stopping times in continuous time).
• TD d'intégration et théorie de la mesure. (Measure and integration theory).
• A brief introduction to self-similar processes.
• Graduate course: Local times and excursion theory for Markov processes.