Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions

We prove existence and uniqueness of solutions to a nonlinear stochastic evolution equation on the $d$-dimensional torus with singular $p$-Laplace-type or total variation flow-type drift with general sublinear doubling nonlinearities and Gaussian gradient Stratonovich noise with divergence-free coefficients. Assuming a weak defective commutator bound and a curvature-dimension condition, the well-posedness result is obtained in a stochastic variational inequality setup by using resolvent and Dirichlet form methods and an approximative It\^{o}-formula.Comment: 26 pages, 58 references. Essential changes to Version 4: Examples revised. Accepted for publication in Stochastic Processes and their Application

Implicit renewal theory for exponential functionals of L\'evy processes

We establish a new functional relation for the probability density function of the exponential functional of a L\'evy process, which allows to significantly simplify the techniques commonly used in the study of these random variables and hence provide quick proofs of known results, derive new results, as well as sharpening known estimates for the distribution. We apply this formula to provide another look to the Wiener-Hopf type factorisation for exponential functionals obtained in a series of papers by Pardo, Patie and Savov, derive new identities in law, and to describe the behaviour of the tail distribution at infinity and of the distribution at zero in a rather large set of situations

Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts

In this paper, a new decay estimate for a class of stochastic evolution equations with weakly dissipative drifts is established, which directly implies the uniqueness of invariant measures for the corresponding transition semigroups. Moreover, the existence of invariant measures and the convergence rate of corresponding transition semigroup to the invariant measure are also investigated. As applications, the main results are applied to singular stochastic $p$-Laplace equations and stochastic fast diffusion equations, which solves an open problem raised by Barbu and Da Prato in [Stoc. Proc. Appl. 120(2010), 1247-1266].Comment: http://www.math.washington.edu/~ejpecp/ECP/viewarticle.php?id=2308&layout=abstrac

Technology shocks and the business cycle

Technology ; Business cycles

pp→A→Zhpp\to A\to Zh and the wrong-sign limit of the Two-Higgs-Doublet Model

We point out the importance of the decay channels $A\to Zh$ and $H\to VV$ in the wrong-sign limit of the Two-Higgs-Doublet Model (2HDM) of type II. They can be the dominant decay modes at moderate values of $\tan\beta$, even if the (pseudo)scalar mass is above the threshold where the decay into a pair of top quarks is kinematically open. Accordingly, large cross sections $pp\to A\to Zh$ and $pp\to H\to VV$ are obtained and currently probed by the LHC experiments, yielding conclusive statements about the remaining parameter space of the wrong-sign limit. In addition, mild excesses - as recently found in the ATLAS analysis $b\bar b \to A\to Zh$ - could be explained. The wrong-sign limit makes other important testable predictions for the light Higgs boson couplings.Comment: 19 pages, 6 figures, v2: journal versio