Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

Hydrodynamic interaction between two vertical cylinders in water waves

The hydrodynamic interaction between two vertical cylinders in water waves is investigated based on the linearized potential flow theory. One of the two cylinders is fixed at the bottom while the other is articulated at the bottom and oscillates with small amplitudes in the direction of the incident wave. Both the diffracted wave and the radiation wave are studied in the present paper. A simple analytical expression for the velocity potential on the surface of each cylinder is obtained by means of Graf's addition theorem. The wave-excited forces and moments on the cylinders, the added masses and the radiation damping coefficients of the oscillating cylinder are all expressed explicitly in series form. The coefficients of the series are determined by solving algebraic equations. Several numerical examples are given to illustrate the effects of various parameters, such as the separation distance, the relative size of the cylinders, and the incident angle, on the first-order and steady second-order forces, the added masses and radiation-damping coefficients as well as the response of the oscillating cylinder.

Compact difference approximation with consistent boundary condition

For simulating multi-scale complex flow fields it should be noted that all the physical quantities we are interested in must be simulated well. With limitation of the computer resources it is preferred to use high order accurate difference schemes. Because of their high accuracy and small stencil of grid points computational fluid dynamics (CFD) workers pay more attention to compact schemes recently. For simulating the complex flow fields the treatment of boundary conditions at the far field boundary points and near far field boundary points is very important. According to authors' experience and published results some aspects of boundary condition treatment for far field boundary are presented, and the emphasis is on treatment of boundary conditions for the upwind compact schemes. The consistent treatment of boundary conditions at the near boundary points is also discussed. At the end of the paper are given some numerical examples. The computed results with presented method are satisfactory.

Evolution and propagation of density waves on galactic disk .2. An approximation of the thin transition layer

In this part of the present work, a simplified model—the thin transition layer theory is proposed. The comparison of this model with the G-L sheet model is made.

Second-best tax policy in a growing economy with externalities

This paper investigates the exploitation of environmental resources in a growing economy within a second-best scal policy framework. Agents derive utility from two types of consumption goods one which relies on an environmental input and one which does not as well as from leisure and from environmental amenity values. Property rights for the environmental resource are potentially incomplete. We connect second best policy to essential components of utility by considering the elasticity of substitution among each of the four utility arguments. The results illustrate potentially important relationships between environmental amentity values and leisure. When amenity values are complementary with leisure, for instance when environmental amenities are used for recreation, taxes on extractive goods generally increase over time. On the other hand, optimal taxes on extractive goods generally decrease over time when leisure and environmental amenity values are substitutes. Unders some parameterizations, complex dynamics leading to nonmonotonic time paths for the state variables can emerge.

Agricultural Best Management Practices and Treatment Wetlands in the Gabilan Watershed: Project Asessment and Evaluation Plan

Several local groups have come together for this project to addresses water quality concerns in the Gabilan Watershed – also known as the Reclamation Ditch Watershed (Fig. 1.1). These are Moss Landing Marine Laboratories (MLML), the Resource Conservation District of Monterey County (RCDMC), Central Coast Watershed Studies (CCoWS), Return of the Natives (RON), Community Alliance with Family Farmers (CAFF), and Coastal Conservation and Research (CC&R). The primary goal is to reduce non-point source pollution – particularly suspended sediment, nutrients, and pesticides – and thereby improve near-shore coastal waters of Moss Landing Harbor and the Monterey Bay. (Document contains 33 pages)