scholarly journals Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Caibin Zeng ◽  
Qigui Yang ◽  
Junfei Cao
Keyword(s):  
Gaussian Noise ◽  
Existence And Uniqueness ◽  
Variational Approach ◽  
Nonlinear Operator ◽  
Random Dynamical System ◽  
Fractional Gaussian Noise ◽  
Infinite Dimensional ◽  
Laplacian Equation ◽  
Variational Solutions ◽  
Monotonicity Conditions

This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficientΦ:dX(t)=A(X(t))dt+Φ(t)dBH(t), whereAis a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalizedp-Laplacian equation.

scholarly journals A NOTE ON VARIATIONAL SOLUTIONS TO SPDE PERTURBED BY GAUSSIAN NOISE IN A GENERAL CLASS

2009 ◽  
Vol 12 (02) ◽  
pp. 353-358
Author(s):  
MICHAEL RÖCKNER ◽  
YI WANG
Keyword(s):  
Hilbert Space ◽  
Gaussian Noise ◽  
Stochastic Partial Differential Equations ◽  
General Class ◽  
Existence And Uniqueness ◽  
Nonlinear Operators ◽  
Infinite Dimensional ◽  
Variational Solutions ◽  
Cylindrical Wiener Process ◽  
Monotonicity Conditions

This note deals with existence and uniqueness of (variational) solutions to the following type of stochastic partial differential equations on a Hilbert space [Formula: see text][Formula: see text] where A and B are random nonlinear operators satisfying monotonicity conditions and G is an infinite dimensional Gaussian process adapted to the same filtration as the cylindrical Wiener process W(t),t ≥ 0.

RANDOM DIFFERENTIAL EQUATIONS WITH RANDOM DELAYS

2011 ◽  
Vol 11 (02n03) ◽  
pp. 369-388 ◽  
Author(s):  
M. J. GARRIDO-ATIENZA ◽  
A. OGROWSKY ◽  
B. SCHMALFUSS
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Random Dynamical System ◽  
Random Delay ◽  
Random Differential Equation ◽  
Autonomous Case ◽  
Random Differential Equations ◽  
Uniqueness Of A Solution

We investigate a random differential equation with random delay. First the non-autonomous case is considered. We show the existence and uniqueness of a solution that generates a cocycle. In particular, the existence of an attractor is proved. Secondly we look at the random case. We pay special attention to the measurability. This allows us to prove that the solution to the random differential equation generates a random dynamical system. The existence result of the attractor can be carried over to the random case.

scholarly journals Generalized Wavelet Fisher’s Information of1/fαSignals

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Julio Ramírez-Pacheco ◽  
Homero Toral-Cruz ◽  
Luis Rizo-Domínguez ◽  
Joaquin Cortez-Gonzalez
Keyword(s):  
Fisher Information ◽  
Gaussian Noise ◽  
Structural Breaks ◽  
Wavelet Domain ◽  
Fractional Gaussian Noise ◽  
Domain Definition ◽  
Potential Applications ◽  
Definition Of ◽  
The Time Domain ◽  
Fisher's Information

This paper defines the generalized wavelet Fisher information of parameterq. This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for1/fαsignals are determined and a detailed discussion of their properties, characteristics and their relationship with waveletq-Fisher information are given. Information planes of1/fsignals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary1/fsignals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of theF-statistic.

scholarly journals Existence and Uniqueness of Solutions to the Wage Equation of Dixit-Stiglitz-Krugman Model with No Restriction on Transport Costs

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlinear Operator ◽  
Sufficient Conditions ◽  
Wage Equation ◽  
Discrete Equation ◽  
Transport Costs ◽  
Economic Activities ◽  
Uniqueness Of Solutions ◽  
Double Nonlinear

In spatial economics, the distribution of wages is described by a solution to the wage equation of Dixit-Stiglitz-Krugman model. The wage equation is a discrete equation that has a double nonlinear singular structure in the sense that the equation contains a discrete nonlinear operator whose kernel itself is expressed by another discrete nonlinear operator with a singularity. In this article, no restrictions are imposed on the maximum of transport costs of the model and on the number of regions where economic activities are conducted. Applying Brouwer fixed point theorem to this discrete double nonlinear singular operator, we prove sufficient conditions for the wage equation to have a solution and a unique one.

The Capacity of the White Gaussian Noise Channel

1990 ◽  
Vol 4 (3) ◽  
pp. 345-353
Author(s):  
Jerome R. Bretienbach
Keyword(s):  
Channel Capacity ◽  
Gaussian Noise ◽  
White Gaussian Noise ◽  
General Sense ◽  
Infinite Dimensional ◽  
Band Limited ◽  
Arbitrary Noise ◽  
Noise Sequence

The capacity of the white Gaussian noise (WGN) channel is widely stated asS/N0nats/unit time. This conclusion is commonly derived either formally, or from the capacity,Wln(l +S/N0W), of the corresponding band-limited channel with bandwidthW, by takingW→8. In this paper, the WGN channel capacity is instead found directly by treating WGN as an arbitrary noise sequence that whitens in a general sense. In addition, the coding theorems proved make explicit the class of allowable receivers, either finite- or infinite-dimensional correlation receivers, or unconstrained. The capacities for these three receiver classes are found to be, respectively:S/N0forS> 0, and 0 forS= 0; and 8 for allS≥ 0. In those cases where the capacity is infinite, actual transmitter–receiver pairs are specified that achieve capacity.

scholarly journals Existence and Uniqueness of Solutions for the p(x)-Laplacian Equation with Convection Term

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1768
Author(s):  
Bin-Sheng Wang ◽  
Gang-Ling Hou ◽  
Bin Ge
Keyword(s):  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Convection Term ◽  
Pseudomonotone Operators ◽  
Uniqueness Of Solutions ◽  
Laplacian Equation ◽  
Uniqueness Of The Solution ◽  
Gradient Based ◽  
Surjectivity Result ◽  
Quasilinear Elliptic

In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results.

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