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 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...

This paper presents the probability hypothesis density (PHD) filter for sets of trajectories. The resulting filter, which is referred to as trajectory probability density filter (TPHD), is capable of estimating trajectories in a principled way without requiring to evaluate all measurement-to-target association hypotheses. As the PHD filter, the TPHD filter is based on recursively obtaining the ...

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...