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<p>Since the zero-noise limitation of invariant measure for stochastic dynamical systems can be described by the viscosity vanishing limitation of stationary Fokker-Planck equations, we study the <i>L</i><sup>1</sup>(ℝ<sup><i>d</i></sup>) and <i>L</i><sup>∞</sup>(ℝ<sup><i>d</i></sup>) exponential decay estimates of stationary Fokker-Planck equations generated by quasi-gradient stochastic dynamical systems in this paper. The exponential decay results are gotten from the energy structure of initial stochastic equation and the Nash-Moser iteration, which have their own important meanings and will also give a solid foundation for further researches.</p>

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L∞(ℝd) Exponential Decay Estimates of Stationary Fokker-planck Equations for Stochastic Quasi-gradient Systems

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Fan Gu

摘要

Since the zero-noise limitation of invariant measure for stochastic dynamical systems can be described by the viscosity vanishing limitation of stationary Fokker-Planck equations, we study the L1(ℝd) and L∞(ℝd) exponential decay estimates of stationary Fokker-Planck equations generated by quasi-gradient stochastic dynamical systems in this paper. The exponential decay results are gotten from the energy structure of initial stochastic equation and the Nash-Moser iteration, which have their own important meanings and will also give a solid foundation for further researches.