Existence of optimal controls for SPDE with locally monotone coefficients

SPDE in Hilbert Space with Locally Monotone Coefficients

The aim of this paper is to extend the usual framework of SPDE with monotone coefficients to include a large class of cases with merely locally monotone coefficients. This new framework is conceptually not more involved than the classical one, but includes many more fundamental examples not included previously. Thus our main result can be applied to various types of SPDEs such as stochastic rea...

Existence of Optimal Controls for Variance Control

The question of the existence of optimal controls is fundamental to many further developments in control theory, and there is a huge literature on the subject. For stochastic control, variance control problems have received much attention recently owing to their importance in nancial mathematics. The existence question is answered in much the same way as it is when only the drift is controlled....

Continuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity

Semilinear stochastic evolution equations with multiplicative L'evy noise are considered‎. ‎The drift term is assumed to be monotone nonlinear and with linear growth‎. ‎Unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎As corollaries of ...

Existence of optimal controls for systems driven by FBSDEs

Existence of optimal controls for a free boundary problem

For Larry Markus on the occasion of his 70 th birthday. ABSTRACT: We consider a model for the radially symmetric evolution (by accretion or dissolution) of the interface between a `pure' solid grain and a liquid solution of the same substance with diiusion both of material and heat. After analyzing the direct problem, we show existence of optimal controls .