Search results for "Stationary sequence"

showing 4 items of 4 documents

Representation of Strongly Stationary Stochastic Processes

1993

A generalization of the orthogonality conditions for a stochastic process to represent strongly stationary processes up to a fixed order is presented. The particular case of non-normal delta correlated processes, and the probabilistic characterization of linear systems subjected to strongly stationary stochastic processes are also discussed.

Continuous-time stochastic processMathematical optimizationStochastic processGeneralizationMechanical EngineeringLinear systemStationary sequenceCondensed Matter PhysicsOrthogonalityMechanics of MaterialsLocal timeStatistical physicsGauss–Markov processMathematicsJournal of Applied Mechanics
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Explicit form of the time operator of a gaussian stationary process

2004

We present the time operator theory in the framework of stationary stochastic processes. The main results of the paper is the derivation of the time operator acting on the Fock space associated with a discrete time gaussian stationary process.

Semi-elliptic operatorStationary processPhysics and Astronomy (miscellaneous)Multiplication operatorGeneral MathematicsMathematical analysisDisplacement operatorOrnstein–Uhlenbeck processStationary sequenceShift operatorMathematicsOrder of integration
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Stationary and non-stationary probability density function for non-linear oscillators

1997

A method for the evaluation of the stationary and non-stationary probability density function of non-linear oscillators subjected to random input is presented. The method requires the approximation of the probability density function of the response in terms of C-type Gram-Charlier series expansion. By applying the weighted residual method, the Fokker-Planck equation is reduced to a system of non-linear first order ordinary differential equations, where the unknowns are the coefficients of the series expansion. Furthermore, the relationships between the A-type and C-type Gram-Charlier series coefficient are derived.

Stationary distributionCharacteristic function (probability theory)Applied MathematicsMechanical EngineeringMathematical analysisProbability density functionStationary sequencestochastic non-linear dynamics; Gram-Charlier expansions; approximate probability density functionGram-Charlier expansionsMechanics of Materialsstochastic non-linear dynamicsProbability distributionProbability-generating functionapproximate probability density functionSeries expansionRandom variableMathematics
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Exact stationary solution for a class of non-linear systems driven by a non-normal delta-correlated process

1995

In this paper the exact stationary solution in terms of probability density function for a restricted class of non-linear systems under both external and parametric non-normal delta-correlated processes is presented. This class has been obtained by imposing a given probability distribution and finding the corresponding dynamical system which satisfies the modified Fokker-Planck equation. The effectiveness of the results has been verified by means of a Monte Carlo simulation.

Stochastic processApplied MathematicsMechanical EngineeringMonte Carlo methodProbability density functionStationary sequenceDynamical systemMechanics of MaterialsApplied mathematicsProbability distributionFokker–Planck equationStatistical physicsMathematicsParametric statisticsInternational Journal of Non-Linear Mechanics
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