Stochastic Modeling

The stochastic modeling group consists of the following faculty within the mathematics department:

Professors Bennett Eisenberg, Soutir Bandyopadhyay, Daniel Conuse, Wei-Min Huang, Garth Isaak, Robert Neel, Ping-Shi Wu, and Joseph E. Yukich.

During the last several years , these faculty have written over a dozen research papers with Lehigh colleagues in the following research areas, described by research topic and associated department. The group has also served on over a dozen doctoral committees.

The stochastic modeling group runs bi-weekly seminar series (Stochastic & Statistical Modelling Seminar) open to the campus and the greater Lehigh Valley. The group is available for both formal and informal technical consulting.

**Network Modeling** [Electrical Engineering Dept]

In future broadband networks based on Asynchronous Transfer Mode (ATM) transmission and switching technology, the dominant kind of impairment is expected to be packed losses. The use of Forward Error Correction (FEC) codes has been proposed as a way to overcome these losses. However, the maximum length of a lost packet string that a packet loss recovery scheme can be designed to recover highly depends upon the temporal behavior between the adjacent packet loss bursts. A realistic model for describing the packet loss process is studied.

**Sampling Problems in Survey Research** [Sociology Dept]

Consider the set of people who attend any day of a multi-day event. Using daily sampling, methods are developed for estimating the proportion of people of a given type when the number of visits by members of different types differs.

**Modeling of fiber bundles [**Mechanical Engineering Dept]

Empirical process methods are used to describe the limit distribution for the tensile strength of fiber bundles consisting of parallel and continuous fibers under equal load sharing.

**Financial Mathematics** [Economics Dept, Finance]

Research analyzes the stochastic models for forward prices for utility companies. Models investigate the type of process which drives forward prices of non-storable goods.

**Modeling the creep and fracture of solids** [Mechanical Engineering Dept]

Research projects are in the following areas:

- description of probabilistic models for the growth of creep cavitation in metals and ceramics.
- use of the finite element method for the probabilistic creep of solids.
- research in fracture mechanics through an analysis of the Hui-Reidel equation.

**Models in medicine** [Merck research Lab; St. Luke's Hospital]

Approximate entropy applies to medical applications; AIDS modeling; Correlation in Diabetes.

**Numerical Analysis** [Engineering, Computer Science] Second derivative formulas for use in the numerical method of lines.