We prove that a class of stochastic differential equations with multiplicative noise has a unique solution in a noncommutative L2 space associated with a von Neumann algebra. As examples we consider usual L2 on a measure space, Hilbert-Schmidt operators and a hyperfinite II1-factor. A problem of finding an inverse of the solution is then discussed. Finally, we explain how a stochastic different...

sar (synthetic aperture radar) image enhancement and segmentation is purpose of this thesis. sar image segmentation is a primary step before steps such as classification and target recognition. the main obstacle in sar image segmentation is inherent speckle noise. speckle noise is a multiplicative and highly destructive noise which results to intensity inhomogeneity. hence common segmentation m...

In many situations, in all branches of physics, one encounters the power-like behavior of some variables, which is best described by a Tsallis distribution characterized by a nonextensivity parameter q and scale parameter T . However, there exist experimental results that can be described only by a Tsallis distributions, which are additionally decorated by some log-periodic oscillating factor. ...

Locally optimum detectors for weak random signals are derived for a generalized observation model incorporating signal-dependent and multiplicative noise. It is shown that the locally optimum random-signal detectors in the generalized observation model are interesting generalizations of those that would be obtained in the purely additive noisy signal model. Examples of explicit results for the ...

We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of Itô stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are shown to be mean-square A-stable for the usual complex scalar linear test problem with multiplicative noise and improve significantly the stabil...

We prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh– Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.

We present a picture of phase transitions of the system with colored multiplicative noise. Considering the noise amplitude as the power– law dependence of the stochastic variable xa we show the way to phase transitions disorder–order and order–disorder. The governed equations for the order parameter and one-time correlator are obtained and investigated in details. The long–time asymptotes in th...

In this paper we study the asymptotic dynamics of the stochastic strongly damped wave equation with multiplicative noise under homogeneous Dirichlet boundary condition. We investigate the existence of a compact random attractor for the random dynamical system associated with the equation.

The Boussinesq equation is a mathematics model of thermohydraulics, which consists of equations of fluid and temperature in the Boussinesq approximation.The deterministic case has been studied systematically by many authors (e.g., see [1– 3]). However, in many practical circumstances, small irregularity has to be taken into account.Thus, it is necessary to add to the equation a random force, wh...

The existence and uniqueness of solutions to the two-dimensional stochastic magneto-hydrodynamic system is established in the presence of either a multiplicative noise or an additive fractional Brownian noise. The method of monotonicity is employed when the noise is multiplicative. In the case of a fractional Brownian noise, a unique mild solution of the system is established under suitable con...