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November 2015 Pathwise nonuniqueness for the SPDEs of some super-Brownian motions with immigration
Yu-Ting Chen
Ann. Probab. 43(6): 3359-3467 (November 2015). DOI: 10.1214/14-AOP962


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.


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Yu-Ting Chen. "Pathwise nonuniqueness for the SPDEs of some super-Brownian motions with immigration." Ann. Probab. 43 (6) 3359 - 3467, November 2015.


Received: 1 August 2013; Revised: 1 July 2014; Published: November 2015
First available in Project Euclid: 11 December 2015

zbMATH: 1337.60135
MathSciNet: MR3433584
Digital Object Identifier: 10.1214/14-AOP962

Primary: 60H15 , 60J68
Secondary: 35K05 , 35R60

Keywords: continuous decomposition , immigration , Stochastic partial differential equations , Super-Brownian motion

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.43 • No. 6 • November 2015
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