Hölder Index for Density States of (α, 1, Β)-superprocesses at a given Point
نویسنده
چکیده
A Hölder regularity index at given points for density states of (α, 1, β)-superprocesses with α > 1 + β is determined. It is shown that this index is strictly greater than the optimal index of local Hölder continuity for those density states.
منابع مشابه
Optimal Hölder Index for Density States of Superprocesses with (1 + Β)-branching Mechanism
For 0 < α ≤ 2, a super-α-stable motion X in R with branching of index 1 + β ∈ (1, 2) is considered. If d < α/β, a dichotomy for the density of states Xt at fixed times t > 0 holds: the density function is locally Hölder continuous if d = 1 and α > 1 + β, but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal Hölder index.
متن کاملOptimal Local Hölder Index for Density States of Superprocesses with (1 + Β)-branching Mechanism
For 0 < α ≤ 2, a super-α-stable motion X in R with branching of index 1+β ∈ (1, 2) is considered. Fix arbitrary t > 0. If d < α/β, a dichotomy for the density function of the measure Xt holds: the density function is locally Hölder continuous if d = 1 and α > 1 + β, but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local Hölder index.
متن کاملOptimal local Hölder index for density states of superprocesses with 1+-branching mechanism
Received May 2008; revised April 2009. Supported by the German Israeli Foundation for Scientific Research and Development, Grant G-807-227.6/2003. AMS 2000 subject classifications. Primary 60J80; secondary 60G57.
متن کاملA class of random measures and their fractal geometry
Typical random measures Ξ belonging to our class are • occupation measures of stable subordinators with stability index 0 < α < 1, • states of a Dawson-Watanabe superprocesses in R, d ≥ 2, • intersection local times of two Brownian paths in R, d = 2, 3. Very roughly, with some modification in the critical cases d = 2, the following basic common properties of these examples can be identified: • ...
متن کاملA super - stable motion with infinite mean branching ✩
A class of finite measure-valued càdlàg superprocesses X with Neveu’s (1992) continuous-state branching mechanism is constructed. To this end, we start from certain supercritical (α, d,β)-superprocesses X(β) with symmetric α-stable motion and (1+β)-branching and prove convergence on path space as β ↓ 0. The log-Laplace equation related to X has the locally non-Lipschitz function u logu as non-l...
متن کامل