We show that the no betting characterisation of the existence of common priors over finite type spaces extends only partially to improper priors in the countably infinite state space context: the existence of a common prior implies the absence of a bounded agreeable bet, and the absence of a common improper prior implies the existence of a bounded agreeable bet. However, a type space that lacks...

In formulating the stability problem for an infinite chain of cars, state space is traditionally taken to be the Hilbert space l2, wherein the displacements of cars from their equilibria, or the velocities from their equilibria, are taken to be square summable. But this obliges the displacements or velocity perturbations of cars that are far down the chain to be vanishingly small and leads to a...

In formulating the stability problem for an infinite chain of cars, state space is traditionally taken to be the Hilbert space `, wherein the displacements of cars from their equilibria, or the velocities from their equilibria, are taken to be square summable. But this obliges the displacements or velocity perturbations of cars that are far down the chain to be vanishingly small and leads to an...

We give an overview of various Lanczos/Krylov space methods and how they are being used for solving certain problems in Control Systems Theory based on state-space models. The matrix methods used are based on Krylov sequences and are closely related to modern iterative methods for standard matrix problems such as sets of linear equations and eigenvalue calculations. We show how these methods ca...

one of the most important economic factors is potential output. in macroeconomic models and structural studies, the estimation of potential output is necessary for projections and analyzing policy performances. there exist several methods for estimating potential output. meanwhile, its estimation is a difficult and complicated matter. empirical studies and researches show that using various tec...

In the present paper, a new 2-D Van der Polstructural oscillator model is introduced for the vortex induced vibrations of circular cylinders.The main purpose of this task is to control the recently introduced model by means of modern control definitions in state space. In order to control the system, the whole model is linearized about its equilibrium point by deriving state-space matrices. The...