Journal ArticleDOI
Stochastic Dynamics of Nonlinear Systems Driven by Non-normal Delta-Correlated Processes
Mario Di Paola,Giovanni Falsone +1 more
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In this article, a new interpretation of the stochastic differential calculus allows first a full explanation of the presence of the Wong-Zakai or Stratonovich correction terms in the Ito's differential rule, and then this rule is extended to take into account the nonnormality of the input.Abstract:
In this paper, nonlinear systems subjected to external and parametric non-normal delta-correlated stochastic excitations are treated. A new interpretation of the stochastic differential calculus allows first a full explanation of the presence of the Wong-Zakai or Stratonovich correction terms in the Ito’s differential rule. Then this rule is extended to take into account the non-normality of the input. The validity of this formulation is confirmed by experimental results obtained by Monte Carlo simulations.read more
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Ito and Stratonovich integrals for delta-correlated processes
Mario Di Paola,Giovanni Falsone +1 more
TL;DR: In this paper, the generalization of the Itd and Stratonovich integrals for the case of non-linear systems excited by parametric delta-correlated processes is presented.
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Linearization in Analysis of Nonlinear Stochastic Systems: Recent Results—Part I: Theory
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Exact stationary solution for a class of non-linear systems driven by a non-normal delta-correlated process
TL;DR: In this paper, the exact stationary solution in terms of probability density function for a restricted class of nonlinear systems under both external and parametric non-normal delta-correlated processes is presented.
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The Estimates of the Mean First Exit Time of a Bistable System Excited by Poisson White Noise
Journal ArticleDOI
Stochastic Energetics for Non-Gaussian Processes
TL;DR: By introducing a new stochastic integral, this work introduces a decomposition of the total energy difference into the work and the heat for each trajectory, and derives a formula to calculate the heat from experimental data on the dynamics.