Jeffrey Collamore: Large excursions and conditioned paths for recursive sequences generated by random matrices

Tid: On 2018-11-14 kl 15.15

Föreläsare: Jeffrey Collamore (Department of Mathematical Science, KU)

Plats: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University

ABSTRACT: Stochastic recursive sequences arise in a variety of contexts in pure and applied probability, with diverse applications to branching processes, risk theory, financial times series modelling, and computer science. It this talk, we consider the multivariate recursive sequence V(n) =M(n)V(n-1)+Q(n), where {M(n)} is an i.i.d. sequence of random matrices and {Q(n)} an i.i.d. sequence of random vectors. Motivated by multi-type branching processes in random environments, this process was first introduced and studied in a seminal work by Kesten (1973). If {M(n)} is ``contracting,’’ then {V(n)} converges in distribution to V, and it is well-known that V exhibits Pareto-type tails. Our objective is to go beyond these classical estimates and to develop more refined path properties for the process {V(n)}, utilizing methods from large deviation theory and applied probability. We describe the time and path of a large exceedance and develop, in particular, a characterization of the conditional distribution under a rare excursion which follows along the lines of the Gibbs conditioning principle.     (Based on joint collaborations with S. Mentemeier and A.N. Vidyashankar.)
Tillhör: Institutionen för matematik
Senast ändrad: 2018-11-08