Historical processes

The Continuum random tree II: an overview

“…For a random tree distributed as CBP(n) this becomes a random sequence (X*(i)); we also have the height profile process (H(j)) as in section 2.2. Rescale as 11 = a-2(n) E H(j), s > 0 (15) j<a(n)s and = a-1(n)X*([2a2(n)s]), -oo < s < oo. (16) Theorem 5 For CBP(n), as n -+ 00 (X; ; -oo < s < 00) (2v-1B87 -oo < s < oo)…”

Avoiding-Probabilities For Brownian Snakes and Super-Brownian Motion

“…For references on superprocesses, see e.g. the monographs and lecture notes by Dawson [3], Dawson-Perkins [5] and Dynkin [10] and the references therein. Let (µ t ) t≥0 denote a super-Brownian motion with branching mechanism 2u 2 (just as in Le Gall [17], Theorem 2.3) started from the finite positive measure ν on R d under the probability measure P ν .…”

Super Fractional Brownian Motion, Fractional Super Brownian Motion and Related Self-Similar (Super) Processes

“…The first is a straightforward application of Theorem 7.13 of Dawson and Perkins (1991), and describes the weak convergence of a particle system of BMT's to HBMT.…”