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
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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.
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Activities and results
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