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arXiv · 1607.05531

Invariants of Fokker-Planck equations

Sumiyoshi Abe
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Abstract

A weak invariant of a stochastic system is defined in such a way that its expectation value with respect to the distribution function as a solution of the associated Fokker-Planck equation is constant in time. A general formula is given for time evolution of fluctuations of the invariants. An application to the problem of share price in finance is illustrated. It is shown how this theory makes it possible to reduce the growth rate of the fluctuations.

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Sumiyoshi Abe. 2016-07-19. Invariants of Fokker-Planck equations. https://doi.org/10.1140/epjst%2Fe2016-60215-1

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