• This paper applies the Asymmetric Autoregressive Conditional Duration (AACD) model to estimate the probability of informed trading (PIN). • We model trade direction (buy versus sell orders) and the duration between trades jointly. • Extending the Easley, Hvidkjaer and O'Hara (2002) approach, which uses the aggregate numbers of daily buy and sell orders to estimate PIN, we use transaction data. • We allow for interactions between consecutive buy-sell orders. • We account for the duration between trades and the volume of trade.

We show that the Perron-Frobenius equation of microscopic chaos based on double symmetric maps leads to an inhomogeneous Smoluchowski equation with a source term. Our perturbative analysis reveals that the source term gives rise to a directed current for a strongly damped particle in a spatially periodic potential. In addition, our result proves that in the zeroth-order limit, the position distribution of the particle obeys the Smoluchowski equation even though the fluctuating force is deterministic.

We consider the resonant effects of chaotic fluctuations on a strongly damped particle in a bistable potential driven by weak sinusoidal perturbation. We derive analytical expressions of chaos-induced transition rate between the neighboring potential wells based on the inhomogeneous Smoluchowski equation. Our first-order analysis reveals that the transition rate has the form of the Kramers escape rate except for a perturbed prefactor. This modification to the prefactor is found to arise from the statistical asymmetry of the chaotic noise. By means of the two-state model and the chaos-induced transition rate, we arrive at an analytical expression of the signal-to-noise ratio (SNR). Our first-order SNR shows that chaotic resonance can correspond directly to stochastic resonance.