The Annals of Probability
- Ann. Probab.
- Volume 43, Number 6 (2015), 3359-3467.
Pathwise nonuniqueness for the SPDEs of some super-Brownian motions with immigration
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.
Ann. Probab., Volume 43, Number 6 (2015), 3359-3467.
Received: August 2013
Revised: July 2014
First available in Project Euclid: 11 December 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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
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