The starting point for this paper is the well known equivalence between convolution filtering with a rescaled Gaussian and the solution of the heat equation. In the first sections we analyze the equivalence between multiscale convolution filtering, linear smoothing methods based on continuous wavelet transforms and the solutions of linear diffusion equations. I.e. we determine a wavelet ψ, resp...

This article adresses parameter estimation with moment-based stochastic filters that only heed the first two moments of the state densities. This approximation provides good results in numerous cases. However, due to missing linear correlation between diffusion parameters and expected states, Bayesian estimation of diffusion parameters such as volatility is not possible. While other filters ove...

The error diffusion halftoning method preserves details well, but produces some unwanted regular texture patterns. The purpose of this paper is to introduce certain nonlinear operators with small kernels for the error diffusion to reduce the regular patterns. The goal is to suppress pattern artifacts while maintaining a small neighborhood. The method employed uses nonlinear diffusion operators,...

We consider optimal investment problems for a diffusion market model with nonobservable random drifts that evolve as an Itô’s process. Admissible strategies do not use direct observations of the market parameters, but rather use historical stock prices. For a non-linear problem with a general performance criterion, the optimal portfolio strategy is expressed via the solution of a scalar minimiz...

Estimation of optical flow and physically motivated brightness changes can be formulated as parameter estimation in linear models. Accuracy of this estimation heavily depends on the filter families used to implement the models. In this paper we focus on models whose terms are all data dependent and therefore are best estimated via total-least-squares (TLS) or similar estimators. Using three dif...

In this paper we consider the issue of distributed adaptive estimation over sensor networks. To deal with more realistic scenario, different variance for observation noise is assumed for sensors in the network. To solve the problem of different variance of observation noise, the proposed method is divided into two phases: I) Estimating each sensor’s observation noise variance and II) using the ...

A brief presentation of the basic concepts in quantum probability theory is given in comparison to the classical one. The notion of quantum white noise, its explicit representation in Fock space, and necessary results of noncommutative stochastic analysis and integration are outlined. Algebraic differential equations that unify the quantum non Markovian diffusion with continuous non demolition ...