Sufficient conditions for a real-valued Gaussian random field X = {X(t), t ∈ RN} with stationary increments to be strongly locally nondeterministic are proven. As applications, small ball probability estimates, Hausdorff measure of the sample paths, sharp Hölder conditions and tail probability estimates for the local times of Gaussian random fields are established. Running head: Strong Local No...

The aim of this paper is to determine how the place of a player in a network of communications ̊ affects her bargaining power with respect to the others. We adapt the Rubinstein-Stahl two-player noncooperative bargaining game of alternating offers to the case of n players connected through a graph. We show that this game has a unique stationary subgame perfect equilibrium outcome from which we d...

We analyze an optimal control problem for the stationary two-dimensional Boussinesq system with controls taken in space of regular Borel measures. Such measure-valued are known to produce sparse solutions. First-order and second-order necessary sufficient optimality conditions established. Following optimize-then-discretize strategy, corresponding finite element approximation will be solved by ...

Vector-valued, asymptotically stationary stochastic processes on r-compact locally compact abelian groups are studied. For such processes, we introduce a stationary spectral measure and show that it is discrete if and only if the asymptotically stationary covariance function is almost periodic. Using an “almost periodic Fourier transform” we recover the discrete part of the spectral measure and...