## The Annals of Probability

### Pathwise nonuniqueness for the SPDEs of some super-Brownian motions with immigration

Yu-Ting Chen

#### Abstract

We prove pathwise nonuniqueness in the stochastic partial differential equations (SPDEs) for some one-dimensional super-Brownian motions with immigration. In contrast to a closely related case investigated by Mueller, Mytnik and Perkins [Ann. Probab. 42 (2014) 2032–2112], the solutions of the present SPDEs are assumed to be nonnegative and have very different properties including uniqueness in law. In proving possible separation of solutions, we derive delicate properties of certain correlated approximating solutions, which is based on a novel coupling method called continuous decomposition. In general, this method may be of independent interest in furnishing solutions of SPDEs with intrinsic adapted structure.

#### Article information

Source
Ann. Probab., Volume 43, Number 6 (2015), 3359-3467.

Dates
Revised: July 2014
First available in Project Euclid: 11 December 2015

https://projecteuclid.org/euclid.aop/1449843633

Digital Object Identifier
doi:10.1214/14-AOP962

Mathematical Reviews number (MathSciNet)
MR3433584

Zentralblatt MATH identifier
1337.60135

#### Citation

Chen, Yu-Ting. Pathwise nonuniqueness for the SPDEs of some super-Brownian motions with immigration. Ann. Probab. 43 (2015), no. 6, 3359--3467. doi:10.1214/14-AOP962. https://projecteuclid.org/euclid.aop/1449843633

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