Functional SPDE with Multiplicative Noise and Dini Drift

2015/05/26 by Xing Huang, F. Y. Wang, Huang, X. +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1505.06890

openalex publication_date 2015/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Existence, uniqueness and non-explosion of the mild solution are proved for a class of semi-linear functional SPDEs with multiplicative noise and Dini continuous drifts. In the finite-dimensional and bounded time delay setting, the log-Harnack inequality and L²-gradient estimate are derived. As the Markov semigroup is associated to the functional (segment) solution of the equation, one needs to make analysis on the path space of the solution in the time interval of delay.

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