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

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