## Electronic Journal of Probability

### Stochastic evolution equations with Wick-polynomial nonlinearities

#### Abstract

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 $C_0-$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.

#### Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 116, 25 pp.

Dates
Accepted: 30 October 2018
First available in Project Euclid: 24 November 2018

https://projecteuclid.org/euclid.ejp/1543028704

Digital Object Identifier
doi:10.1214/18-EJP241

#### Citation

Levajković, Tijana; Pilipović, Stevan; Seleši, Dora; Žigić, Milica. Stochastic evolution equations with Wick-polynomial nonlinearities. Electron. J. Probab. 23 (2018), paper no. 116, 25 pp. doi:10.1214/18-EJP241. https://projecteuclid.org/euclid.ejp/1543028704

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