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T. Levajković, S. Pilipovic, D. Selesi, M. Zigic:
"Stochastic evolution equations with Wick-polynomial nonlinearities";
Electronic Journal of Probability, 23 (2018), S. 116 - 140.

We study nonlinear parabolic stochastic partial differential equations with Wick-power and Wick-polynomial type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fujita equation, the stochastic Fisher-KPP equation and the stochastic FitzHugh-Nagumo equation among many others. By implementing the theory of C0−semigroups and evolution systems into the chaos expansion theory in infinite dimensional spaces, we prove existence and uniqueness of solutions for this class of SPDEs. In particular, we also treat the linear nonautonomous case and provide several applications featured as stochastic reaction-diffusion equations that arise in biology, medicine and physics.

Hida-Kondratiev spaces, stochastic nonlinear evolution equations, Wick product, infinitesimal generator

http://dx.doi.org/10.1214/18-EJP241

https://publik.tuwien.ac.at/files/publik_276615.pdf