Stochastic incompleteness for graphs and weak Omori-Yau maximum principle

We prove an analogue of the weak Omori-Yau maximum principle and Khas'minskii's criterion for graphs in the general setting of Keller and Lenz. Our approach naturally gives the stability of stochastic incompleteness under certain surgeries of graphs. It allows to develop a unified approach to all known criteria of stochastic completeness/incompleteness, as well as to obtain new criteria.Comment: Revised version. We add some previously omitted proo

A Second Order Fully-discrete Linear Energy Stable Scheme for a Binary Compressible Viscous Fluid Model

We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible fluid flow mixtures derived from the generalized Onsager Principle. The hydrodynamic model not only possesses the variational structure, but also warrants the mass, linear momentum conservation as well as energy dissipation. We first reformulate the model in an equivalent form using the energy quadratization method and then discretize the reformulated model to obtain a semi-discrete partial differential equation system using the Crank-Nicolson method in time. The numerical scheme so derived preserves the mass conservation and energy dissipation law at the semi-discrete level. Then, we discretize the semi-discrete PDE system on a staggered grid in space to arrive at a fully discrete scheme using the 2nd order finite difference method, which respects a discrete energy dissipation law. We prove the unique solvability of the linear system resulting from the fully discrete scheme. Mesh refinements and two numerical examples on phase separation due to the spinodal decomposition in two polymeric fluids and interface evolution in the gas-liquid mixture are presented to show the convergence property and the usefulness of the new scheme in applications

Is the forward bias economically small? Evidence from European rates.

For the purpose of testing uncovered interest parity (UIP), rates of European currencies against the DEM offer a distinct advantage: ERM membership or informal ERM association induces statistically significant mean-reversion in weekly rates. Thus, unlike for freely floating rates, there is an expectations signal that has nontrivial variation and is sufficiently traceable for research purposes. When running the standard regression tests of the unbiased-expectations hypothesis at the one-week horizon, we nevertheless obtain essentially zero coefficients for intra-EMS exchange rates (and the familiar negative coefficients for extra-EMS rates). Even more puzzlingly, lagged exchange rate changes remain significant when added to the regression, a feature that seems harder to explain as a missing-variable effect. The deviation from UIP is significant not just statistically but also economically: trading-rule tests reveal that for sufficiently large filters the average profit per trade exceeds transaction costs, and that cumulative gains can be quite impressive. The size of the profits and the patterns from buy versus sell decisions also allow us to reject the risk premium and the Peso hypotheses as separately sufficient explanations.Bias; Costs; Currency; Decision; Decisions; EMS; ERM; Exchange rates; Forward bias; Hypotheses; Risk; Size; Trade; Trading rule; Transaction cost; International; Finance;