2016/07/31 by Sumiyoshi Abe · 7 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Astronomy #Fokker–Planck equation #Mathematical analysis #Mathematical physics #Mathematics #Partial differential equation #Physics #Planck #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #cond-mat.stat-mech #physics.class-ph
paper · pdf · doi:10.1140/epjst/e2016-60215-1
published in The European Physical Journal Special Topics 226(3), 529-532 (Springer Science+Business Media) · 8 pages, no figures. Published version
openalex publication_date 2017/02/01 · arxiv created 2017/03/18 · arxiv updated 2017/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.