Computation of Fokker-Planck equation
Author:
Stephen S.-T. Yau
Journal:
Quart. Appl. Math. 62 (2004), 643-650
MSC:
Primary 82C31; Secondary 82D10, 94A12
DOI:
https://doi.org/10.1090/qam/2104266
MathSciNet review:
MR2104266
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Abstract: In plasma physics, the interaction of radio-frequency waves with a plasma is described by a Fokker-Planck equation with an added quasilinear term. In nonlinear filtering with conditional probability density of the state ${x_t}$ given the observation $\left \{ {y\left ( s \right ):0 \le s \le t} \right \}$ is also described by a Fokker-Planck equation with an added first order term. Method for solving Fokker-Planck equation by means of ordinary differential equations is discussed.
N. J. Fisch, Confining a Tokamak Plasma with $rf$-Driven currents, Phys. Rev. Lett. 41 (1978), 873–876.
C. F. F. Karney, Fokker-Planck and Quasilinear Codes, Computer Physics Reports 4 (1983), 183.
G. D. Kerbel and M. G. McCoy, Kinetic theory and simulation of multispecies plasmas in tokamaks excited with electromagnetic waves in the ion-cyclotron range of frequencies, Phys. Fluids, vol. 28 (1985), 3629–3649.
G. Q. Hu and S. S.-T. Yau, Finite dimensional filters with nonlinear drift XV: New direct method for construction of universal finite dimensional filter, (to appear) IEEE Transactions on Aerospace and Electronic Systems.
- Shing-Tung Yau and Stephen S.-T. Yau, Real time solution of nonlinear filtering problem without memory. I, Math. Res. Lett. 7 (2000), no. 5-6, 671–693. MR 1809293, DOI https://doi.org/10.4310/MRL.2000.v7.n6.a2
N. J. Fisch, Confining a Tokamak Plasma with $rf$-Driven currents, Phys. Rev. Lett. 41 (1978), 873–876.
C. F. F. Karney, Fokker-Planck and Quasilinear Codes, Computer Physics Reports 4 (1983), 183.
G. D. Kerbel and M. G. McCoy, Kinetic theory and simulation of multispecies plasmas in tokamaks excited with electromagnetic waves in the ion-cyclotron range of frequencies, Phys. Fluids, vol. 28 (1985), 3629–3649.
G. Q. Hu and S. S.-T. Yau, Finite dimensional filters with nonlinear drift XV: New direct method for construction of universal finite dimensional filter, (to appear) IEEE Transactions on Aerospace and Electronic Systems.
S. T. Yau and S. S.-T. Yau, Real time solution of nonlinear filtering problem without memory I, Mathematical Research Letters 7 (2000), 671–693.
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Article copyright:
© Copyright 2004
American Mathematical Society
