Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 582-595.

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Local Times of the Solution to Stochastic Heat Equation with Fractional Noise

Zhi Wang1(),Litan Yan2(),Xianye Yu3,*()   

  1. 1 School of Sciences, Ningbo University of Technology, Zhejiang Ningbo 315211
    2 Department of Mathematics, College of Science, Donghua University, Shanghai 201620
    3 School of Mathematics, Sun Yat-sen University, Guangzhou 510275
  • Received:2017-11-02 Online:2019-06-26 Published:2019-06-27
  • Contact: Xianye Yu;;
  • Supported by:
    the NSFC(11701304);the NSFC(11571071);the NSFC(11701589);the Zhejiang Provincial Natural Science Foundation(LQ16A010006);the Fundamental Research Funds for the Central Universities(171gpy17)


In this paper, we study the collision and intersection local times of the solution to stochastic heat equation with additive fractional noise. We mainly prove its existence and smoothness properties through local nondeterminism and chaos expansion.

Key words: Stochastic heat equation, Fractional noise, Collision local time, Intersection local time, Chaos expansion

CLC Number: 

  • O211.6