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The branching property can be summarised into the fact that given her type and birth time, the daughter process of any individual born is independent of all individuals not in
This result has consequences for the Hausdorff dimension of the frontier of planar Brownian motion, and also for the Hausdorff dimension of the set of cut-points of planar
The Ewens-Pitman two-parameter family of exchangeable partitions Π α,θ of an infinite set has be- come a central model for species sampling (see [ 7, 18 ] for extensive background
Here is intuitive idea behind this construction: Since we conditioned on a large block of 1’s to occur in the true scenery ξ close to the origin, observing a long block of 1’s at
the coupling: once the processes X t and Y t have coupled, they can either move together until one of them hits the boundary ( sticky mirror coupling - this is in fact the
Keywords: Martingale, submartingale, distribution function, tail inequality, differential subordina- tion, conditional differential
Key words: semimartingales; Gaussian processes; stationary processes; moving averages; stochastic convolutions; non-canonical representations.. AMS 2000 Subject Classification:
We have shown that it is possible to extend the integral in a unique way from all sim- ple A -measurable integrands (which are in a one-to-one correspondence with the
