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On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums

Tran Loc HungPhan Tri KienNguyen Tan Nhut — 2019

Kybernetika

Geometric random sums arise in various applied problems like physics, biology, economics, risk processes, stochastic finance, queuing theory, reliability models, regenerative models, etc. Their asymptotic behaviors with convergence rates become a big subject of interest. The main purpose of this paper is to study the asymptotic behaviors of normalized geometric random sums of independent and identically distributed random variables via Gnedenko's Transfer Theorem. Moreover, using the Zolotarev probability...

Adjoint methods for obstacle problems and weakly coupled systems of PDE

Filippo CagnettiDiogo GomesHung Vinh Tran — 2013

ESAIM: Control, Optimisation and Calculus of Variations

The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton − Jacobi equations, and weakly coupled systems of obstacle type. In particular, new results about the speed of convergence of some approximation procedures are derived.

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