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SUMMARY:Andrzej Święch (Georgia Institute of Technology)
DTSTART:20210422T140000Z
DTEND:20210422T150000Z
DTSTAMP:20260423T005756Z
UID:RJWAPDE/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RJWAPDE/24/"
 >Singular perturbations and optimal control of stochastic systems in infin
 ite dimension</a>\nby Andrzej Święch (Georgia Institute of Technology) a
 s part of Rio de Janeiro webinar on analysis and partial differential equa
 tions\n\n\nAbstract\nWe will discuss a stochastic optimal control problem 
 for a two scale system driven by an infinite dimensional stochastic differ
 ential equation which consists of ''slow'' and ''fast'' components. We wil
 l consider a rather general case where the evolution is given by an abstra
 ct semilinear stochastic differential equation with nonlinear dependence o
 n the controls. We will present a PDE approach to the problem based on the
  theory of viscosity solutions in Hilbert spaces. This approach allows to 
 prove that as the speed of the fast component goes to infinity\, the value
  functions of the optimal control problems converge to the viscosity solut
 ion of a reduced effective equation. Our results generalize to the infinit
 e dimensional case the finite dimensional results of Alvarez and Bardi and
  complement recent results in Hilbert spaces obtained by Guatteri and Tess
 itore.\n
LOCATION:https://researchseminars.org/talk/RJWAPDE/24/
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