Wick differential and Poisson equations associated to the 𝚀𝚆𝙽-Euler operator acting on generalized operators

2016 ◽  
Vol 66 (6) ◽  
Author(s):  
Hafedh Rguigui
Keyword(s):  
Differential Equation ◽  
White Noise ◽  
Poisson Equations ◽  
Euler Operator

AbstractIn this paper we study the homogeneous Wick differential equation associated to the quantum white noise (𝚀𝚆𝙽) Euler operator

Composition and invariance methods for solving some stochastic control problems

1975 ◽  
Vol 7 (02) ◽  
pp. 299-329 ◽  
Author(s):  
V. E. Beneš
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamical Systems ◽  
White Noise ◽  
Stochastic Control ◽  
Analytical Methods ◽  
Control Problems ◽  
Numerical Treatment ◽  
Partial Differential ◽  
Stochastic Control Problems

This paper considers certain stochastic control problems in which control affects the criterion through the process trajectory. Special analytical methods are developed to solve such problems for certain dynamical systems forced by white noise. It is found that some control problems hitherto approachable only through laborious numerical treatment of the non-linear Bellman-Hamilton-Jacobi partial differential equation can now be solved.

Time Series Methods for the Synthesis of Random Vibration Systems

1976 ◽  
Vol 43 (1) ◽  
pp. 159-165 ◽  
Author(s):  
W. Gersch ◽  
R. S-Z. Liu
Keyword(s):  
Differential Equation ◽  
Time Series ◽  
White Noise ◽  
Least Squares ◽  
Discrete Time ◽  
Covariance Function ◽  
Structural System ◽  
Covariance Functions ◽  
Discrete Time Series ◽  
Scalar Output

A least-squares method procedure for synthesizing the discrete time series that is characteristic of the uniform samples of the response of linear structural systems to stationary random excitation is described. The structural system is assumed to be an n-degree-of-freedom system that is representable by a set of ordinary differential equations excited by a vector white noise force. It is known that the discrete time series of uniformly spaced samples of a scalar white noise excited stationary linear differential equation can be represented as an autoregressive-moving average (AR-MA) time series and that the parameters of the AR-MA model can be computed from the covariance function of the differential equation model. The contributions of this paper are (i) the result that a scalar input scalar output AR-MA model duplicates the scalar output covariance function of a regularly sampled linear structural system with a multivariate white noise input, (ii) a computationally efficient method for computing the covariance function of a randomly excited structural system, and (iii) a demonstration of the theory and the numerical details of a two-stage least-squares procedure for the computation of the AR-MA parameters from the output covariance functions data.

QWN-EULER OPERATOR AND ASSOCIATED CAUCHY PROBLEM

2012 ◽  
Vol 15 (01) ◽  
pp. 1250004 ◽  
Author(s):  
ABDESSATAR BARHOUMI ◽  
HABIB OUERDIANE ◽  
HAFEDH RGUIGUI
Keyword(s):  
Cauchy Problem ◽  
Integral Representation ◽  
White Noise ◽  
Coordinate System ◽  
Functional Integral ◽  
Euler Operator ◽  
The Cauchy Problem ◽  
Sum Formula

In this paper the quantum white noise (QWN)-Euler operator [Formula: see text] is defined as the sum [Formula: see text], where [Formula: see text] and NQ stand for appropriate QWN counterparts of the Gross Laplacian and the conservation operator, respectively. It is shown that [Formula: see text] has an integral representation in terms of the QWN-derivatives [Formula: see text] as a kind of functional integral acting on nuclear algebra of white noise operators. The solution of the Cauchy problem associated to the QWN-Euler operator is worked out in the basis of the QWN coordinate system.

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