MODELLING OF HIGH-DIMENSIONAL DIFFUSION STOCHASTIC PROCESS WITH NONLINEAR COEFFICIENTS FOR ENGINEERING APPLICATIONS — PART II: APPROXIMATIONS FOR COVARIANCE AND SPECTRAL DENSITY OF STATIONARY PROCESS
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Publication:4799023
DOI10.1142/S0218202599000555zbMath1009.60067OpenAlexW2091781708MaRDI QIDQ4799023
Yevgeny V. Mamontov, Magnus Willander
Publication date: 16 March 2003
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0218202599000555
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MODELLING OF HIGH-DIMENSIONAL DIFFUSION STOCHASTIC PROCESS WITH NONLINEAR COEFFICIENTS FOR ENGINEERING APPLICATIONS — PART I: APPROXIMATIONS FOR EXPECTATION AND VARIANCE OF NONSTATIONARY PROCESS ⋮ The generalized kinetic modelling of a multicomponent ``real-life fluid by means of a single distribution function ⋮ Stochastic continuum mechanics -- a thermodynamic-limit-free alternative to statistical mechanics: equilibrium of isothermal ideal isotropic uniform fluid. ⋮ Modelling complex systems in applied sciences; methods and tools of the mathematical kinetic theory for active particles ⋮ Stochastic mechanics in the context of the properties of living systems ⋮ The sea-wave elevation and multistability in a non-autonomous nonlinear Itô's stochastic differential equation for the rolling angle of a ship ⋮ An analytical-numerical method for fast evaluation of probability densities for transient solutions of nonlinear Itô's stochastic differential equations ⋮ Nonstationary invariant distributions and the hydrodynamics-style generalization of the Kol\-mo\-gorov-forward/Fokker-Planck equation ⋮ Thermomechanical effects in the flow of a fluid in porous media ⋮ Optimization of traffic flow conditions by minimization of quadratic functionals ⋮ A specification of the Maxwell-Rayleigh-Heisenberg approach to modelling fluids for bioelectronic applications
Cites Work
- Long asymptotic correlation time for non-linear autonomous Itô's stochastic differential equation
- Spectral density of a nonlinear single-degree-of-freedom system's response to a white-noise random excitation: A unique case of an exact solution
- Power Spectral Density of Nonlinear System Response: The Recursion Method
- The spectral density of the nonlinear damping model: single DOF case
- The spectral density of a nonlinear damping model: multi-DOF case
- MODELLING OF HIGH-DIMENSIONAL DIFFUSION STOCHASTIC PROCESS WITH NONLINEAR COEFFICIENTS FOR ENGINEERING APPLICATIONS — PART I: APPROXIMATIONS FOR EXPECTATION AND VARIANCE OF NONSTATIONARY PROCESS
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