6533b854fe1ef96bd12af4f0

RESEARCH PRODUCT

Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior

Leonid MytnikAchim Klenke

subject

Statistics and ProbabilityPure mathematicsProbability (math.PR)coexistenceType (model theory)Characterization (mathematics)Branching (polymer chemistry)Trotter productstochastic differential equationsLévy noisesegregation of typesStochastic differential equationKernel (algebra)Mutually catalytic branching60G1760K35Convergence (routing)FOS: Mathematics60J6560J55PreprintStatistics Probability and UncertaintyMathematics - ProbabilityMathematicsBranching process

description

Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479-497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.

yearjournalcountryeditionlanguage
2012-01-01The Annals of Probability
https://doi.org/10.1214/10-aop621