Large Deviations for Small Noise Diffusions in a Fast Markovian Environment

A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a finite state pure jump process. Previous works have considered settings where the coupling between the components is weak in a certain sense. In the current work we study a fully coupled system in which the drift and diffusion coefficient of the slow component and the jump intensity function and jump distribution of the fast process depend on the states of both components. In addition, the diffusion can be degenerate. Our proofs use certain stochastic control representations for expectations of exponential functionals of finite dimensional Brownian motions and Poisson random measures together with weak convergence arguments. A key challenge is in the proof of the large deviation lower bound where, due to the interplay between the degeneracy of the diffusion and the full dependence of the coefficients on the two components, the associated local rate function has poor regularity properties.Comment: 42 page

Macroeconomic Conditions and Business Exit: Determinants of Failures and Acquisitions of UK Firms

We study the impact of macroeconomic instability on business exit in a world where acquisition and bankruptcy are co-determined. Our objective is to discover how the processes that determine bankruptcies and acquisitions depend on the macroeconomic environment, particularly, macroeconomic instability. To this end we estimate competing risks hazard regression models using data on UK quoted firms spanning a thirty-eight year period that witnessed several business cycles. We find that macroeconomic instability has opposite effects on bankruptcy hazard and acquisition hazard, raising the former and lowering the latter. While it is not surprising that bankruptcy hazard is counter-cyclical and acquisition hazard pro-cyclical, it is noteworthy that the US business cycle is a better predictor of UK acquisitions and bankruptcies than the UK cycle itself.Bankruptcy, Acquisitions, Macroeconomic Instability, Competing Risks, Cox Proportional Hazards Model.

Constraints on Dark Matter-Neutrino Interaction from 21-cm Cosmology and Forecasts on SKA1-Low

In this article, we have done a thorough investigation of the possible effects of interaction between dark matter (DM) and neutrinos on reionization history. We have constrained the interaction strength using 21 cm Cosmology and found out possible deviations from standard, non-interacting $\Lambda$CDM scenario. Comparing the results with the existing constraints from present cosmological observations reveals that 21 cm observations are more competent to constrain the interaction strength by a few orders of magnitude. We have also searched for prospects of detecting any such interaction in the upcoming 21 cm mission SKA1-Low by doing a forecast analysis and error estimation.Comment: Version considerably modified. To appear in MNRA