[ABE-L] Seminário de Probabilidade - IM-UFRJ - 11 de maio

[Maria Eulalia Vares]

Dear colleagues,

Our next seminar will be held on Monday, May 11, from *3:30 p.m. to 4:30
p.m.* (Rio de Janeiro local time). The meeting will take place at *room
C116 - Bloco C - CT – Instituto de Matemática – UFRJ*. There will be no
transmission online.

*Speaker:* Anderson de Oliveira Calixto (IME-UFF)

*Title:* Multiscale stochastic control with domain restriction in the slow
variable

*Abstract:* Multiscale stochastic optimal control problems arise naturally
in systems whose dynamics evolve on different time scales, posing important
analytical challenges, especially in the presence of state constraints. In
this talk, we consider infinite-horizon multiscale control problems in
which the constraints act on the slow variables.

The formulation leads to a fully nonlinear, degenerate elliptic
Hamilton–Jacobi–Bellman (HJB) equation, supplemented by Neumann boundary
conditions. The analysis combines singular perturbation techniques with the
theory of viscosity solutions, allowing us to derive an effective
description of the problem.

In particular, we identify the effective HJB equation and establish uniform
convergence on compact sets of the multiscale value functions to the
corresponding limiting value function. The limiting equation characterizes
an effective stochastic control problem driven only by the slow dynamics,
with the influence of the fast variables incorporated through a
homogenization procedure.

This is joint work with Glauco Valle (IM-UFRJ) and Bernardo Freitas Paulo
da Costa (EMAp-FGV).

More complete information about the seminars can be found at:
https://ppge.im.ufrj.br/seminarios-de-probabilidade/

Sincerely,

Giulio Iacobelli and Maria Eulalia Vares
-- 
Maria Eulalia Vares
Professora Titular - Instituto de Matemática - UFRJ
Coordenadora do Programa de Pós-Graduação em Estatística
https://ppge.im.ufrj.br/
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