Existence, uniqueness and statistical theory of turbulent solutions of the stochastic Navier-Stokes equation, in three dimensions -- an overview.
We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. In the strongly damped case, the propagator is shown to admit an expansion in terms of the finitely many eigenmodes near the real axis, with an error exponentially decaying in time. In the presence of an elliptic closed geodesic not meeting the support of the damping coefficient, we show that there exists a sequence of eigenfrequencies converging rapidly to the real axis. In the case of Zoll manifolds,...
In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation () based Sharpe ratio for measuring...
Despite their deficiencies, continuous second-order traffic flow models are still commonly used to derive discrete-time models that help traffic engineers to model and predict traffic oflow behaviour on highways. We brie fly overview the development of traffic flow theory based on continuous flow-density models of Lighthill-Whitham-Richards (LWR) type, that lead to the second-order model of Aw-Rascle. We will then concentrate on widely-adopted discrete approximation to the LWR model by Daganzo's...