6533b7cffe1ef96bd12598ac
RESEARCH PRODUCT
Direct Derivation of Corrective Terms in SDE Through Nonlinear Transformation on Fokker–Planck Equation
Antonina PirrottaMario Di Paolasubject
Kushner equationDifferential equationApplied MathematicsMechanical EngineeringNonlinear transformationMathematical analysisFirst-order partial differential equationFokker-Planck equationAerospace EngineeringOcean EngineeringPoisson inputItô's calculuIntegrating factorStochastic partial differential equationStochastic differential equationQuantum stochastic calculusControl and Systems EngineeringApplied mathematicsFokker–Planck equationStochastic differential calculusElectrical and Electronic EngineeringMathematicsdescription
This paper examines the problem of probabilistic characterization of nonlinear systems driven by normal and Poissonian white noise. By means of classical nonlinear transformation the stochastic differential equation driven by external input is transformed into a parametric-type stochastic differential equation. Such equations are commonly handled with Ito-type stochastic differential equations and Ito's rule is used to find the response statistics. Here a different approach is proposed, which mainly consists in transforming the Fokker–Planck equation for the original system driven by external input, in the transformed probability density function of the new state variable. It will be shown that the Wong–Zakay or Stratonovich corrective term and the hierarchy of correction terms in the case of Poissonian white noise arise in a natural way.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-06-01 | Nonlinear Dynamics |