Summary
In this note stochastic calculus is used to characterise multiplicative excessive functions of a binary branching Brownian motion with a constant creation rate. Some properties of the martingales given by invariant functions are studied. In particular, it is seen that these positive and unbounded martingales tend a.s. to 0 and are not square integrable. Informally speaking, they exhibit a clustering phenomenon in the underlying supercritical branching Brownian motion.
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This work was done while the author was visiting the University of British Columbia, Mathematical Department, and was partly supported by a NSERC grant. AMS 1980 subject classifications: primary 60J80, 60J65 secondary 60J60
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Salminen, P. On multiplicative excessive functions of a branching Brownian motion. Probab. Th. Rel. Fields 85, 43–56 (1990). https://doi.org/10.1007/BF01377627
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DOI: https://doi.org/10.1007/BF01377627
Keywords
- Stochastic Process
- Brownian Motion
- Probability Theory
- Mathematical Biology
- Invariant Function