Related papers: A probabilistic approach to second order variation…
In this paper we deal with a second order nonlinear evolution inclusion, with a nonmonotone, noncoercive viscosity term. Using a parabolic regularization (approximation) of the problem and {\it a priori} bounds that permit passing to the…
We consider a zero-sum stochastic differential game over elementary mixed feed-back strategies. These are strategies based only on the knowledge of the past state, randomized continuously in time from a sampling distribution which is kept…
In this paper, the problem of stability in terms of two measures is considered for a class of stochastic partial differential delay equations with switching. Sufficient conditions for stability in terms of two measures are obtained based on…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical…
We study the behaviour of solutions of ordinary differential equations of the second order with singular points, where the coefficients of the second-order derivative vanishes. In particular, we consider solutions entering a singular point…
We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an…
The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality without any smallness assumptions on the gap between growth and coercitivity…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Riemannian geometry. The results are new and extend…
In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under…
We prove that boundary value problems for fully nonlinear second-order parabolic equations admit $L_{p}$-viscosity solutions, which are in $C^{1+\alpha}$ for an $\alpha\in(0,1)$. The equations have a special structure that the "main" part…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…
We study nested variational inequalities, which are variational inequalities whose feasible set is the solution set of another variational inequality. We present a projected averaging Tikhonov algorithm requiring the weakest conditions in…
We provide sufficient conditions for the existence of invariant probability measures for generic stochastic differential equations with finite time delay. This is achieved by means of the Krylov-Bogoliubov method. Furthermore, we focus on…
We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…
In this paper, we introduce and study a stochastic differential variational inequality (SDVI) which consists of a stochastic differential equation and a stochastic variational inequality. We obtain the existence and uniqueness of the…
The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order…
We formulate the flow of thick fluids as evolution variational and quasi-variational inequalities, with a variable threshold on the absolute value of the deformation rate tensor. In the variational case, we show the existence and uniqueness…