Random time modifications of stochastic processes with numerical aspects for non-linear equations

National research project founded by the UEFISCDI (Ministerul Cercetarii si Inovarii, Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii)

PN-III-P1-1.1-PD-2016-0293

 

Project leader: Oana-Valeria STAMATE (LUPASCU)

Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy

Abstract

 
The project presents stochastic analysis techniques which are of interest for recent developments in partial differential equations, motivated by applications to branching processes and by numerical aspects. We investigate potential kernels generating sub-Markovian resolvents, in connection with a new approach for the Blumenthal-Getoor-McKean Theorem on the time changed Markov processes with the inverse of a continuous additive functional. We give a probabilistic numerical approach for the nonlinear Dirichlet problem associated with a branching process describing the time evolution of a system of particles rather than of a one single particle. We develop a procedure to treat numerically the Neumann problem on balls for the Laplace operator, by means of the killed Brownian motion, based on a recent emphasized representation of the solution of the Neumann problem in terms of the solution of an associated Dirichlet problem. Finally, we investigate the time changed fractional Brownian motion by means of a positive-valued stationary stochastic process with independent nonnegative increments.

 

Activities and results

Articles:

 

  • L. Beznea, M. Deaconu, O. Lupaşcu-Stamate, Scaling property for fragmentation processes related to avalanches. In: Applications of Mathematics and Informatics in Natural Sciences and Engineering, Springer Proceedings in Mathematics & Statistics 334 (2020), https://doi.org/10.1007/978-3-030-56356-1_3
  • L. Beznea, A-M. Boeangiu, O. Lupaşcu-Stamate, h-transform of Doob and nonlocal branching processes, Anal. Math. Phys. 10 (2020), no 4, 47.
  • L. Beznea, O. Lupașcu-Stamate, C. Vrabie, Stochastic solutions to evolution equations of non-local branching processes, Nonlinear Analysis 200 (2020), 112021, 18 pp.
  • O. Lupaşcu-Stamate, C.-A Tudor, Rosenblatt Laplace motion, Mediterr. J. Math., 16 (2019), Article number: 15.
  • I. R. Ionescu, O. Lupaşcu-Stamate, Boundary variation method for the generalized Cheeger problem, Applied Numerical Mathematics 140 (2019), 199-214.
 

Preprints:

  • D. Coculescu, O. Lupascu-Stamate, G. Visentin, Emergence and Evolution of Cooperation for Survival: a Continuous Time Model, Preprint 2020.

Talks at international conferences:

  • Statistical Modeling with Application, Bucharest, online workshop, November 2020 (invited talk)
  • Atelier de travail en Stochastique et EDP, Bucharest, online workshop, October 2020 (invited talk)
  • The 38th “Caius Iacob” Conference on Fluid Mechanics and its Technical Applications, Bucharest, November 2019
  • The Annual Conference of the Romanian Mathematical Society, Pitesti, Romania, October 2019 (invited talk)
  • Ergotic Theory and Related Fields, Bucharest, October 2019, (invited talk)
  • The Ninth Congress of Romanian Mathematicians, Galati, Romania, June 2019
  • Journees de Probabilités, Dourdan, France, June 2019
  • The 15th Romanian-Finnish seminar, Turku, Finland, June 2019
  • Workshop for Young Researchers in Mathematics (9th edition), Bucharest, June 2019 (invited talk)
 

Research team

Project leader: Oana-Valeria STAMATE (LUPASCU)

Mentor: Prof. Dr. Viorel BARBU

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