A Multi-Resolution Approach to the Fokker-Planck-Kolmogorov Equation with Application to Stochastic Nonlinear Filtering and Optimal Design

2012 ◽  
Author(s):  
D. Yu ◽  
S. Chakravorty
Keyword(s):  
Optimal Design ◽  
Nonlinear Filtering ◽  
Kolmogorov Equation ◽  
Fokker Planck

A class of nonlinear oscillational systems admitting exact solution of the Fokker-Planck-Kolmogorov equation

1991 ◽  
Vol 43 (10) ◽  
pp. 1282-1286
Author(s):  
Yu. A. Mitropol'skii ◽  
Nguen Tien Kkhiem
Keyword(s):  
Exact Solution ◽  
Kolmogorov Equation ◽  
Fokker Planck

On uniqueness of probability solutions to the Fokker-Planck-Kolmogorov equation

2021 ◽  
Vol 212 (6) ◽  
Author(s):  
Vladimir Igorevich Bogachev ◽  
Tikhon Il'ich Krasovitskii ◽  
Stanislav Valer'evich Shaposhnikov
Keyword(s):  
Kolmogorov Equation ◽  
Fokker Planck

Model for the Suspensions Separation Process in Hydrodynamic Filters with a Rotating Filter Element

2021 ◽  
pp. 48-56
Author(s):  
Vladimir Devisilov ◽  
V. Lvov ◽  
E. Sharay
Keyword(s):  
Theoretical Calculation ◽  
Statistical Method ◽  
Separation Process ◽  
Filter Element ◽  
Kolmogorov Equation ◽  
Diffusion Type ◽  
Self Cleaning ◽  
Fokker Planck

The possibility of applying the probabilistic-statistical method for theoretical calculation of characteristics related to suspensions separation in self-cleaning hydrodynamic filters with a rotating filter element has been demonstrated. It has been shown that the change in characteristics of the suspensions separation in hydrodynamic filters with a rotating filter element can be satisfactorily described based on equations of diffusion type, in particular, using the Fokker–Planck–Kolmogorov equation. The main parameters of the separation process in hydrodynamic filters with a rotating filter element have been determined.

Solutions to the Fokker-Planck-Kolmogorov equation for the van der pol system subjected to periodic and random perturbations

1983 ◽  
Vol 34 (6) ◽  
pp. 635-637
Author(s):  
Nguyen Dong Anh ◽  
Kieu Th� Dyk
Keyword(s):  
Kolmogorov Equation ◽  
Random Perturbations ◽  
Van Der Pol ◽  
Fokker Planck

Transport and evolution of classical and quantum ensembles

2020 ◽  
pp. 292-341
Author(s):  
Sandip Tiwari
Keyword(s):  
Boltzmann Transport Equation ◽  
Planck Equation ◽  
Kolmogorov Equation ◽  
Boltzmann Transport ◽  
Relaxation Time Approximation ◽  
Quantum Mechanical Description ◽  
Probabilistic Evolution ◽  
Fokker Planck Equations ◽  
And Diffusion ◽  
Fokker Planck

This chapter explores the evolution of an ensemble of electrons under stimulus, classically and quantum-mechanically. The classical Liouville description is derived, and then reformed to the quantum Liouville equation. The differences between the classical and the quantum-mechanical description are discussed, emphasizing the uncertainty-induced fuzziness in the quantum description. The Fokker-Planck equation is introduced to describe the evolution of ensembles and fluctuations in it that comprise the noise. The Liouville description makes it possible to write the Boltzmann transport equation with scattering. Limits of validity of the relaxation time approximation are discussed for the various scattering possibilities. From this description, conservation equations are derived, and drift and diffusion discussed as an approximation. Brownian motion arising in fast-and-slow events and response are related to the drift and diffusion and to the Langevin and Fokker-Planck equations as probabilistic evolution. This leads to a discussion of Markov processes and the Kolmogorov equation.

Cooperative target localization using multiple UAVs with out-of-sequence measurements

2017 ◽  
Vol 89 (1) ◽  
pp. 112-119 ◽  
Author(s):  
Xiaogang Wang ◽  
Wutao Qin ◽  
Yuliang Bai ◽  
Naigang Cui
Keyword(s):  
Time Delay ◽  
Probability Density ◽  
Gaussian Noise ◽  
Nonlinear Filtering ◽  
Planck Equation ◽  
Target Localization ◽  
Content Type ◽  
Fokker Planck Equation ◽  
Delay Measurement ◽  
Fokker Planck

Purpose The time delay would occurs when the measurements of multiple unmanned aerial vehicles (UAVs) are transmitted to the date processing center during cooperative target localization. This problem is often named as the out-of-sequence measurement (OOSM) problem. This paper aims to present a nonlinear filtering based on solving the Fokker–Planck equation to address the issue of OOSM. Design/methodology/approach According to the arrival time of measurement, the proposed nonlinear filtering can be divided into two parts. The non-delay measurement would be fused in the first part, in which the Fokker–Planck equation is utilized to propagate the conditional probability density function in the forward form. The time delay measurement is fused in the second part, in which the Fokker–Planck is used in the backward form approximately. The Bayes formula is applied in both parts during the measurement update. Findings Under the Bayesian filtering framework, this nonlinear filtering is not only suitable for the Gaussian noise assumption but also for the non-Gaussian noise assumption. The nonlinear filtering is applied to the cooperative target localization problem. Simulation results show that the proposed filtering algorithm is superior to the previous Y algorithm. Practical implications In this paper, the research shows that a better performance can be obtained by fusing multiple UAV measurements and treating time delay in measurement with the proposed algorithm. Originality/value In this paper, the OOSM problem is settled based on solving the Fokker–Planck equation. Generally, the Fokker–Planck equation can be used to predict the probability density forward in time. However, to associate the current state with the state related to OOSM, it would be used to propagate the probability density backward either.

Approximate solution of the Fokker-Planck-Kolmogorov equation

1995 ◽  
Vol 47 (3) ◽  
pp. 408-419 ◽  
Author(s):  
Yu. A. Mitropol'skii
Keyword(s):  
Approximate Solution ◽  
Kolmogorov Equation ◽  
Fokker Planck
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