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作者：ALBEVERIO, S; MOLCHANOV, SA; SURGAILIS, D
作者单位：Vilnius University; University of North Carolina; University of North Carolina Charlotte
摘要：The model of the potential turbulence described by the 3-dimensional Burgers' equation with random initial data was developped by Zeldovich and Shandarin, in order to explain the existing Large Scale Structure of the Universe. Most of the recent probabilistic investigations of large time asymptotics of the solution deal with the central limit type results (the ''Gaussian scenario''), under suitable moment assumptions on the initial velocity field. These results and some open questions are disc...
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作者：HOHNLE, R; STURM, KT
作者单位：University of Erlangen Nuremberg
摘要：Let (X(t), P-x) be an m-symmetric Markov process with a strictly transition density. Consider the additive functional A(t):= integral(0)(t)f(X(s)) (is where f: E --> [0, infinity] is a universally measurable function on the state space E. Among others, we prove that P-x(A(t) < infinity) = 1, for some x is an element of EE and some t > 0, already implies P-x(A(t) < infinity) = 1, for quasi every x is an element of E and all t > 0. The latter is also equivalent to P-x(A(t) < infinity) > 0, for q...
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作者：LI, XM
摘要：Here we discuss the regularity of solutions of SDE's and obtain conditions under which a SDE on a complete Riemannian manifold M has a global smooth solution flow, in particular improving the usual global Lipschitz hypothesis when M = R(n). There are also results on non-explosion of diffusions.
