56,946 research outputs found

    Strong completeness for a class of stochastic differential equations with irregular coefficients

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    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 tt, the solution flow FtF_t is weakly differentiable and for each p>0p>0 there is a positive number T(p)T(p) such that for all t<T(p)t<T(p), the solution flow Ft(â‹…)F_t(\cdot) 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

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    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 fNLf_{\rm NL}. We illustrate our result in the chain inflation model and the very weakly dissipative warm inflation model. We show that fNL∼O(1)f_{NL}\sim {\cal O}(1) is general in such models. If we allow modified equation of state, or some decoupling effects, the large thermal nonGaussianity of order fNL>5f_{\rm NL}>5 or even fNL∼100f_{\rm NL}\sim 100 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 fNLf_{\rm NL}.Comment: 20 pages, 1 figure. v2, v3: references and acknowledgments update

    On the cohomology of Fano varieties and the Springer correspondence

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