The Annals of Probability

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

Yu-Ting Chen

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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

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

Received: August 2013
Revised: July 2014
First available in Project Euclid: 11 December 2015

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60J68: Superprocesses
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 35K05: Heat equation

Stochastic partial differential equations super-Brownian motion immigration continuous decomposition


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.

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