Critical behavior of some measure-valued processes

✍ Scribed by Klaus Fleischmann

• Publisher: John Wiley and Sons
• Year: 1988
• Tongue: English
• Weight: 879 KB
• Volume: 135
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19881350114

✦ Synopsis

Ab8tmt.t. The so-called wSghted occupation thiio process Y sesociatecl with some critical messurevalaeil branching proeesa is considered. Y has absolutely continuoits sttLtes provided that the tlimension of the phase space is mall enough. The corresponding density fiinctions form a random process ti. In some cases there esists u critical ctimension such that rt. eonsitlered in the space-time c l i n g i m , is R self-similar random non-neptive. field. This self-simit~~r field is infinitely divisible but not stable.

where v is the solution to B

v(t, z)=dv(t, z)-@(t, z), v(0, z}=l-esp[-~(z)]zO, at a v(t, z)= -( -d)"'%(t, z)-vL*qt, z), v(Oy5)=y(2) see DAWSON and IVANOFF [8] or HOLLFN and Smoocx [13].