in this paper, we show that the chapman-kolmogorov formula could be used as a recursive formula for computing the m-step-ahead conditional density of a markov bilinear model. the stationary marginal probability density function of the model may be approximated by the m-step-ahead conditional density for sufficiently large m.

S. Towers State University of New York at Stony Brook Abstract Kernel Probability Density Estimation techniques are fast growing in popularity in the particle physics community. This note gives an overview of these techniques, and compares their signal/background discrimination performance to that of an artificial neural network.

This paper shows how satellite owner/operators may use sequential estimates of collision probability, along with a prior assessment of the base risk of collision, in a compound hypothesis ratio test to inform decisions concerning collision risk mitigation maneuvers. The compound hypothesis test reduces to a simple probability ratio test, which appears to be a novel result. The test satisfies to...

This paper is dedicated to our friend Marek, for his birthday. Two of us know Marek since more than 20 years, when we embarked in the adventure of Mathematics for Finance. Our paths diverged, but we always kept strong ties. Thank you, Marek, for all the fruitful discussions we have had. We hope you will find some interest in this paper and the modeling of credit risk we present, and we are look...

We discussed several techniques for graphical exploratory data analysis in Chapter 5. One purpose of these exploratory techniques is to obtain information and insights about the distribution of the underlying population. For instance, we would like to know if the distribution is multi-modal, skewed, symmetric, etc. Another way to gain understanding about the distribution of the data is to estim...

In order to numerically invert Laplace transforms to calculate probability distributions in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., of a waiting-time distribution) can be computed when the Laplace transform values of component probability density functions (pdf's) (e.g., of a service-tim...

We show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable. We adopt the definition of density entropy as a functional of a distribution density whose time evolution is determined by a transport equation, conceived as the only prescription to use for the calculation. Although the ...

We propose a method of estimation of the derivatives of probability density based on wavelets methods for a sequence of random variables with a common one-dimensional probability density function and obtain an upper bound on Lp-losses for such estimators. We suppose that the process is strongly mixing and we show that the rate of convergence essentially depends on the behavior of a special quad...