Modeling Rate-Modulated Selfexciting Point Processes.
STANFORD UNIV CA DEPT OF ELECTRICAL ENGINEERING
Pagination or Media Count:
This paper addresses several issues arising in the modeling of discrete event processes for which the sample-path evolution depends on the past trajectory and is also controlled by an independent modulating process. While information on local, sample-path evolution is sometimes readily obtainable or measurable, in many applications it is more important to predict ensemble averaged responses to variations in the modulation process. The authors discuss this problem in the framework of a general model for rate-modulated selfexciting processes and, under certain assumptions, derive a nonlinear ordinary differential equation for approximately predicting ensemble behavior from known sample-path evolution laws. A successful application of this method to a neural encoding process has already been made.
- Theoretical Mathematics