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Strong completeness for a class of stochastic differential equations with irregular coefficients
We prove the strong completeness for a class of non-degenerate SDEs, whose
coefficients are not necessarily uniformly elliptic nor locally Lipschitz
continuous nor bounded. Moreover, for each , the solution flow is
weakly differentiable and for each there is a positive number such
that for all , the solution flow belongs to the Sobolev
space W_{\loc}^{1,p}. The main tool for this is the approximation of the
associated derivative flow equations. As an application a differential formula
is also obtained
Inflationary NonGaussianity from Thermal Fluctuations
We calculate the contribution of the fluctuations with the thermal origin to
the inflationary nonGaussianity. We find that even a small component of
radiation can lead to a large nonGaussianity. We show that this thermal
nonGaussianity always has positive . We illustrate our result in
the chain inflation model and the very weakly dissipative warm inflation model.
We show that is general in such models. If we allow
modified equation of state, or some decoupling effects, the large thermal
nonGaussianity of order or even can be
produced. We also show that the power spectrum of chain inflation should have a
thermal origin. In the Appendix A, we made a clarification on the different
conventions used in the literature related to the calculation of .Comment: 20 pages, 1 figure. v2, v3: references and acknowledgments update
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