The stochastic differential equations of many diffusion processes which arise in studies of population growth in random environments can be transformed, if the Stratonovich stochastic calculus is employed, to the equation of the Wiener process. If the transformation function has certain properties then the transition probability density function and quantities relating to the time to first atta...

We investigate the term structure of zero coupon bonds when interest rates are driven by a general marked point process as well as by a Wiener process. Developing a theory which allows for measure-valued trading portfolios we study existence and uniqueness of a martingale measure. We also study completeness and its relation to the uniqueness of a martingale measure. For the case of a finite jum...

The classical solution to the noise removal problem is the Wiener filter, which utilizes the second-order statistics of the Fourier decomposition. Subband decompositions of natural images have significantly non-Gaussian higher-order point statistics; these statistics capture image properties that elude Fourier-based techniques. We develop a Bayesian estimator that is a natural extension of the ...

The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations...

This paper presents a new approach to interest rate dynamics. We consider the general family of arbitrage-free positive interest rate models, valid on all time horizons, in the case of a discount bond system driven by a Brownian motion of one or more dimensions. We show that the space of such models admits a canonical mapping to the space of square-integrable Wiener functionals. This is achieve...

　A new approach is introduced to estimate the formal information of neurons. Formal Information, mainly discusses about the aspects of the response that is related to the stimulus. Estimation is based on introducing a mathematical nonlinear model with Hammerstein-Wiener system estimator. This method of system identification consists of three blocks to completely describe the nonlinearity of inp...

A recursive algorithm is proposed in this paper to identify Hammerstein–Wiener systems with heteroscedastic measurement noise. Based on the parameterization model of Hammerstein–Wiener systems, the algorithm is derived by minimizing the expectation of the sum of squared parameter estimation errors. By replacing the immeasurable internal variables with their estimations, the need for the commonl...

The problem of the identification of Hammerstein and Wiener models is considered in this paper. The suggested approach in this paper utilizes the spectral magnitude matching method that minimizes the sum squared error between the spectral magnitudes evaluated for a number of short-time frames of the measured output signal of the nonlinear system and the output signal of the nonlinear model. The...

This paper presents a stochastic analysis of the Filtered-X LMS algorithm. The mean weight vector recursion is derived for slow adaptation and for a white reference signal without use of independence theory. The Wiener solution is determined explicitly as a function of the input statistics and the impulse responses of the primary and secondary signal paths. It is shown that the steady-state mea...