This thesis consists of two papers which focuses on a particular diffusion type Dirichlet form E(F,G) = ∫ 〈ADF,DG〉H dν, whereA = ∑∞ i=1 λi〈Si, ·〉HSi. Here Si, i ∈ N, is the basis in the Cameron-Martin space, H, consisting of the Schauder functions, and ν denotes the Wiener measure. In Paper I, we let λi, i ∈ N, vary over the space of wiener trajectories in a way that the diffusion operator A is...

A variational representation for positive functionals of a Hilbert space valued Wiener process (W (·)) is proved. This representation is then used to prove a large deviations principle for the family {G (W (·))} >0 where G is an appropriate family of measurable maps from the Wiener space to some Polish space.

In this paper we present a characterization of those Wiener functionals that are the likelihood ratio for a 'signal plus independent noise' model. The characterization is expressed in terms of the representation of such functionals in a series of multiple Wiener integrals. Let {ys, 0 <s =z r} be a random process with measurable sample functions satisfying ] y, ] G K as. Let { Ws, 0 <s < T} be a...

We present an improved denoising method based on filtering of the noisy wavelet coefficients using a Wiener gain for automatic speech recognition (ASR). We optimize the wavelet parameters for speech and different noise profiles to achieve a better estimate of the Wiener gain for effective filtering. Moreover, we introduce a scaling parameter in the Wiener gain to minimize mismatch caused by dis...

Suppose that the signal X to be estimated is a diffusion process in a random medium W and the signal is correlated with the observation noise. We study the historical filtering problem concerned with estimating the signal path up until the current time based upon the back observations. Using Dirichlet form theory, we introduce a filtering model for general rough signal X and establish a multipl...

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...

1. Pearson RK. Selecting nonlinear model structures for computer control. J Process Control 2003; 13: 1–26 2. Bloemen HHJ, Chou CT, van den Boom TJJ, Verdult V, Verhaegen M, Backx TC. Wiener model identification and predictive control for dual composition control of a distillation column. J Process Control 2001; 11: 601–620 3. Westwick D, Verhaegen M. Identifying MIMO Wiener systems using subsp...

We analyze the Rosenblatt process which is a selfsimilar process with stationary increments and which appears as limit in the so-called Non Central Limit Theorem (Dobrushin and Major (1979), Taqqu (1979)). This process is non-Gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-Itô multiple integral with respect to the Brownian motion on a finite interval and...

In the present paper we study moving averages (also known as stochastic convolutions) driven by a Wiener process and with a deterministic kernel. Necessary and sufficient conditions on the kernel are provided for the moving average to be a semimartingale in its natural filtration. Our results are constructive meaning that they provide a simple method to obtain kernels for which the moving avera...

In this paper, a flexible channel allocation strategy with wiener prediction method is proposed for mobile multimedia networks. In this scheme, a set of available channels is divided into fixed and flexible sets and, using wiener prediction technique channels are allocated for multimedia calls. The wiener prediction method uses only the local information for resource allocation. It allows new c...