23 research outputs found
General Extinction Results for Stochastic Partial Differential Equations and Applications
Let be a positive definite self-adjoint operator on the -space
associated to a \si-finite measure space. Let be the dual space of the
domain of w.r.t. . By using an It\^o type inequality for
the -norm and an integrability condition for the hyperbound of the semigroup
P_t:=\e^{-Lt}, general extinction results are derived for a class of
continuous adapted processes on . Main applications include stochastic and
deterministic fast diffusion equations with fractional Laplacians. Furthermore,
we prove exponential integrability of the extinction time for all space
dimensions in the singular diffusion version of the well-known Zhang-model for
self-organized criticality, provided the noise is small enough. Thus we obtain
that the system goes to the critical state in finite time in the deterministic
and with probability one in finite time in the stochastic case.Comment: 19 page
Convergence of operators semigroups generated by elliptic operators
Röckner M, Zhang TS. Convergence of operators semigroups generated by elliptic operators. Osaka Journal of Mathematics. 1997;34(4):923-932
Construction of diffusions on configuration spaces
Ma Z-M, Röckner M. Construction of diffusions on configuration spaces. Osaka Journal of Mathematics. 2000;37(2):273-314
Mehler formula and capacities for infinite-dimensional Ornstein-Uhlenbeck processes with general linear drift
Bogachev VI, Röckner M. Mehler formula and capacities for inifinite dimensional Ornstein-Uhlenbeck processes with General linear drift. Osaka Journal of Mathematics . 1995;32(2):237-274