Abstract
SynopsisWe consider a class of measure-valued Markov processes constructed by taking a superprocess over some underlying Markov process and conditioning it to stay alive forever. We obtain two representations of such a process. The first representation is in terms of an “immortal particle” that moves around according to the underlying Markov process and throws off pieces of mass, which then proceed to evolve in the same way that mass evolves for the unconditioned superprocess. As a consequence of this representation, we show that the tail σ-field of the conditioned superprocess is trivial if the tail σ-field of the underlying process is trivial. The second representation is analogous to one obtained by LeGall in the unconditioned case. It represents the conditioned superprocess in terms of a certain process taking values in the path space of the underlying process. This representation is useful for studying the “transience” and “recurrence” properties of the closed support process.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
