An introduction to Markov processes associated to nonlinear and nonlocal operators
Fecha: Mar, Mayo 30 - Vie, Jun 2 2017
Hora: 10:00
Ponentes: Lucian Beznea, Institute of Mathematics of the Romanian Academy (IMAR)
DATES: 30 May - 2 June 2017 (5 sessions)
TIME: From Tuesday to Friday (10:00 - 12:00) and on Thursday (15:00 - 17:00). A total of 10 hours.
We first introduce basic notions and facts on Markov processes: transition function, associated resolvent, strongly continuous resolvents on L^p spaces, superharmonic functions, reduced function and capacities, jumps modification, infinitesimal local and nonlocal generators. We give two applications to partial differential (and integro-differential) equations: the stochastic solution of the Dirichlet problem and the solution of the martingale problem. Finally, we present relations between two classes of measure-valued Markov processes (superprocesses and processes with nonlocal branching) and nonlinear operators of the form Lu + f(u), where L is a second order elliptic differential operator and f is a "branching mechanism", with applications to nonlinear boundary value problems.
PREREQUISITES: functional analysis and probability, basic knowledge.
*Registration is free, but inscription is required before 25th May: So as to inscribe send an e-mail to roldan@bcamath.org. Student grants are available. Please, let us know if you need support for travel and accommodation expenses.
Organizadores:
BCAM
Ponentes confirmados:
Lucian Beznea, Institute of Mathematics of the Romanian Academy (IMAR)
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