An introduction to Markov processes associated to nonlinear and nonlocal operators

Date: Tue, May 30 - Fri, Jun 2 2017

Hour: 10:00

Speakers: 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.

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Confirmed speakers:

Lucian Beznea, Institute of Mathematics of the Romanian Academy (IMAR)