Personal website of José Alfredo López-Mimbela

Contact:

Centro de Investigación en Matemáticas

Apartado Postal 402, 36000 Guanajuato, Mexico

Phone: +52 473 7327155

Fax: +52 473 7325749

e-mail: jalfredo at cimat.mx

Main Publications

Gorostiza, L.G.; López-Mimbela, J.A. The multitype measure branching process, Advances in Applied Probability, 22 (1990), 49-67.
López-Mimbela, J.A. Fluctuation limits of multitype branching random fields, Journal of Multivariate Analysis, 40 (1992), 56-83.
Gorostiza, L.G.; López-Mimbela, J.A. The demographic variation process of multitype branching random fields, Journal of Multivariate Analysis, 41 (1992), 102-116.
Gorostiza, L.; López-Mimbela, J.A. A convergence criterion for measure-valued processes, and application to continuous superprocesses, Progress in Probability , 32 (1993), 62-71.
Gorostiza, L.G.; López-Mimbela, J.A. An occupation time approach for convergence of measure-valued processes, and the death process of a branching system, Statistics & Probability Letters , 21 (1994), 59-67.
López-Mimbela, J.A.; Wakolbinger, A. Clumping in Multitype Branching Trees, Advances in Applied Probability 28 (1996), 1051-1071.
López-Mimbela, J.A.; Torres, A. Intrinsic ultracontractivity and blowup of a semilinear Dirichlet boundary value problem, Aportaciones Matemáticas, Notas de Investigación 14 (1998), 283-290.
López-Mimbela, J.A.; Wakolbinger, A. Length of Galton-Watson trees and blow up of semilinear systems, Journal of Applied Probability 35 (1998), 802-811.
López-Mimbela, J.A.; Wakolbinger, A. A Probabilistic Proof of Non-explosion of a Non-linear PDE System, Journal of Applied Probability 34 (2000), 635-641.
Birkner, M.; López-Mimbela, J.A.; Wakolbinger, A. Blow-up of semilinear PDE's. A probabilistic approach, Proc. Am. Math. Society 30 (2002), No. 8, 2431-2442.
Birkner, M.; López-Mimbela, J.A.; Wakolbinger, A. Comparison results and steady states for the Fujita equation with fractional Laplacian, Annales de l'Institut Henri Poincare (C) Non Linear Analysis 22, Issue 1, January-February 2005, Pages 83-97.
Kolkovska, E.T.; López-Mimbela, J.A.; Villa, J. Occupation measure and local time of classical risk processes, Insurance Math. Econom. 37 (2005), no. 3, 573-584.
López-Mimbela, J.A.; Privault, N. Blowup and stability of semilinear PDE's with gamma generators, J. Math. Anal. Appl. 307 (2005), no. 1, 181-205.
Kolev, N.; Kolkovska, E.T.; López-Mimbela, J.A. Joint probability generating function for a vector of arbitrary indicator variables,, J. Comput. Appl. Math. 186 (2006), no. 1, 89-98.
López-Mimbela, J.A.; Villa, J. Local time and Tanaka formula for a multitype Dawson-Watanabe superprocess, Math. Nachr. 279 (2006), no. 15, 1695-1708.
López-Mimbela, J.A.; Pérez, A. Finite time blow up and stability of a semilinear equation with a time dependent Lévy generator, Stoch. Models 22 (2006), no. 4, 735-752.
Kolkovska, E.T.; López-Mimbela, J.A. Critical exponents of semilinear equations via the Feynman-Kac formula, Pliska Stud. Math. Bulgar. 18(2007), 165-182.
Kolkovska, E.T.; López-Mimbela, J.A.; Pérez, A. Blowup and life span bounds for a reaction-diffusion equation with a time-dependent generator, Electron. J. Diff. Eqns. , Vol. 2008 (2008), No. 10, pp. 1-18.
Chakraborty, S.; López-Mimbela, J.A. Non-Explosion of a class of semilinear equations via branching particle representations, Adv. in Appl. Probab. 40 (2008), no. 1, 250-272.
López-Mimbela, J.A.; Murillo, A. Law of Large Numbers for the Occupation Time of an Age-dependent Branching System, ALEA: Latin American Journal of Probability and Mathematical Statistics 6 (2009), 115-131.
Dozzi, M.; López-Mimbela, J.A. Finite-Time Blowup and Existence of Global Positive Solutions of a Semi-Linear SPDE, Stochastic Processes and their Applications 120 (2010), 767-776.
Kevei, P.; López-Mimbela, J.A. Critical Multitype Branching Systems: Extinction Result, Electronic Journal of Probability Vol. 16 (2011), Paper no. 50, pages 1356-1380.
López-Mimbela, J.A.; Privault, N. Large time behavior of reaction-diffusion equations with Bessel generators, J. Math. Anal. Appl. 383 (2011), 560-572.
López-Mimbela, J.A.; Wakolbinger, A. Which critically branching populations persist?, Classical and Modern Branching Processes. Editores: K. Athreya and P. Jagers. Springer Lecture Note Series of the Institute for Applied Mathematics, Minneapolis, 1996.
López-Mimbela, J.A.; Villa, J. Existence of self-intersection local time of the multitype Dawson-Watanabe superprocess, Contemporary Mathematics 336 (2003), 213-224.
López-Mimbela, J.A.; Villa, J. Super-Brownian local time: a representation and two applications, J. Math. Sciences (NY) 121, No. 5 (2004), 2653-2663.
López-Mimbela, J.A. Branching particle representation of a class of semilinear equations. Pliska Stud. Math. Bulgar. 16 (2004), 101-119.
López-Mimbela, J.A.; Privault, N. Critical exponents for semilinear PDEs with bounded potentials, Seminar on Stochastic Analysis, Random Fields and Applications. Dalang, R.C., Dozzi, M., Russo, F. (Eds.), Progress in Probability 59 (2008), 243-260.
Chakraborty, S; Kolkovska, E.T.; López-Mimbela, J.A. Stability of a nonlinear equation related to a spatially-inhomogeneous branching process, Progress in Probability 65 (2011), 189-200.
López-Mimbela, J.A.; Murillo, A. Fluctuation limit theorems for age-dependent critical binary branching systems, ESAIM: Proceedings 31 (2011), 55-72.
Dozzi, M.; Kolkovska, E.T.; López-Mimbela, J.A. Exponential Functionals of Brownian Motion and Explosion Times of a System of Semilinear SPDEs, Stochastic Analysis and Applications 31 (2013), 975-991.
Dozzi, M.; Kolkovska, E.T.; López-Mimbela, J.A. Finite-time blowup and existence of global positive solutions of a semi-linear SPDE with fractional noise, Modern Stochastics and Applications. Korolyuk, V.; Limnios, N.; Mishura, Y.; Sakhno, L.; Shevchenko, G. (Eds.) Springer Optimization and Its Applications 90, Springer Verlag 2013.

Submitted Papers

López-Mimbela, J.A.; Pérez, A. Global and nonglobal solutions of a system of nonautonomous semilinear equations with ultracontractive Lévy generators. 2014.
Álvarez, A.; López-Mimbela, J.A.; Privault, N. Asymptotic behavior of a family of semilinear SPDEs with time-dependent coefficients. 2014.

Edited Volumes and Proceedings

Proceedings of the 30th Nation-Wide Congress of Mexican Mathematical Society (jointly with M. Neumann, M. Rzedowski and M. Shapiro).
Modelos Estocásticos II (jointly with D. Hernández and R. Quezada). Aportaciones Matemáticas Serie Investigación 16, Sociedad Matemática Mexicana, 2001.
Proceeding of the Fourth Symposium on Probability and Stochastic Processes (jointly with L.G. Gorostiza and J. León). Aportaciones Matemáticas Serie Investigación 12, México 1996. ISBN: 968-36-3593-8.
Guest Editor of the journal Stochastic Models, Vol 22 (2006), Taylor and Francis.

Undergraduate Students

Sergio Alejandro Muñoz Muratalla, Poisson processes in Euclidean spaces, 2000.
Henri Pantí Trejo, Diffusion approximation in population genetics and in risk theory, 2008.
Yareli Morán Acevedo, How many times and how long is the surplus negative?, 2012.
Guillermo Elías Martínez Dibene, Fundamentals of SDEs and an application to population genetics, 2013.

Master Sc. Students

Alberto Contreras C., Diffusion limits of branching random fields, 1993.
Alejandro Torres, Applications of Markov processes to finite-time blowup of a class of semi-linear equations, 1997.
Marina Suárez Muñoz, Random measures in locally compact spaces, 2006.
Valentina Castellanos, Quasi-stationary distribution of a bivariate Markov chain: application to a genetic model, 2006.
Ma. Elena Hernández, Super-Brownian motion: construction and asymptotic behavior, 2011.
Gerardo Barrera Vargas, Rényi's entropy function of weakly y-mixing dynamical systems, and an application to the large deviations of short-return times, 2011.
Biviana Marcela Suárez, Existence of global and non-global solutions of a semi-linear stochastic equation, 2012.
Eugenio Guerrero Ruiz, Random dynamical systems and their attractors, 2013.

PhD Students

José Villa Morales, Tanaka formula-type representations of the local times of superprocesses, 2002.
Aroldo Pérez Pérez, Explosive and global positive solutions of semi-linear non-autonomous Cauchy problems, 2004.
Antonio Murillo Salas, Limit theorems for critical binary branching age-dependent particle systems with heavy-tailed lifetimes, 2008.

Postdoctoral Students

Santanu Chakraborty (PhD, Indian Statistical Institute), 2004.
Péter Kevei (Hungarian Academy of Sciences), 2011.