Probability Commons^™

Estimating The Probability Of Severe Convective Storms: A Local Perspective For The Central And Northern Plains, Preston W. Leftwich Jr.

National Oceanographic and Atmospheric Administration: Technical Reports and Related Materials

Summary and Conclusions

A procedure to estimate probabilities of the occurrence of severe convective storms within local areas has been described. Probabilities were based on a simulated climatology and the relative frequency of severe convective events when a selected site was contained within an operational Outlook or Watch. Combined data from five local areas were used to develop a general model for local probabilities within the central and northern Plains region. Attachment of probabilities to specific products placed values within a framework familiar to both forecasters and "end-users." Application of results in an operational scenario demonstrated representative local probabilities and …

Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established.

The Stable Manifold Theorem For Stochastic Differential Equations, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow

Articles and Preprints

We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Itô-type equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution. For Stratonovich SDEs, the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating SDE. The proof of the stable manifold theorem is based …

How Do Judges Think About Risk?, W. Kip Viscusi

Vanderbilt Law School Faculty Publications

A sample of almost 100 judges exhibited well-known patterns of biases in risk beliefs and reasonable implicit values of life. These biases and personal preferences largely do not affect attitudes toward judicial risk decisions, though there are some exceptions, such as ambiguity aversion, misinterpretation of negligence rules, and retrospective risk assessments in accident cases, which is a form of hindsight bias. Although judges avoided many pitfalls exhibited by jurors and the population at large, they nevertheless exhibited systematic errors, particularly for small probability-large loss events. These findings highlighted the importance of judicial review and the input of expert risk analysts …