Panqiu Xia

Moment estimates for stochastic PDEs in the sublinear regime

Stochastic partial differential equations (SPDEs) with multiplicative noise exhibit rich phenomena such as intermittency, characterised by rapid growth of moments. Classical results show exponential moment growth when the diffusion coefficient grows linearly, as in the parabolic Anderson model. In this talk, we study the stochastic heat equation in the sublinear regime (super Brownian motion as an example). We present new moment estimates showing that the growth becomes polynomial or subexponential, leading to a notion of smooth intermittency, and discuss results that apply to a broad class of diffusion coefficients and noise structures.

Panqiu Xia is a lecturer in the statistics research group at Cardiff University (since Autumn 2024). Previously, he was a postdoc at Auburn University (USA), under the guidance of Dr. Le Chen, from Autumn 2022 to Summer 2024. Prior to that, from Autumn 2020 to Summer 2022, he worked as a postdoc in the mathematical biology group led by Prof. Carsten Wiuf at the University of Copenhagen (Denmark), following the completion of his Ph.D. in 2020, which was jointly supervised by Prof. Yaozhong Hu and Prof. David Nualart at the University of Kansas (USA) in 2020.

His research interests include both theoretical and applied probability, specifically in the following areas: Malliavin calculus, SPDEs, Stein's method, and chemical reaction networks.