Book contents
- Frontmatter
- Contents
- Preface
- Part I Point Processes
- Part II Optimal Control in Discrete Time
- Part III Optimal Control in Continuous Time
- Part IV Non-Linear Filtering Theory
- 12 Non-Linear Filtering with Wiener Noise
- 13 The Conditional Density
- 14 Non-Linear Filtering with Counting-Process Observations
- 15 Filtering with k-Variate Counting-Process Observations
- Part V Applications in Financial Economics
- References
- Index of Symbols
- Subject Index
14 - Non-Linear Filtering with Counting-Process Observations
from Part IV - Non-Linear Filtering Theory
Published online by Cambridge University Press: 27 May 2021
Book contents
- Frontmatter
- Contents
- Preface
- Part I Point Processes
- Part II Optimal Control in Discrete Time
- Part III Optimal Control in Continuous Time
- Part IV Non-Linear Filtering Theory
- 12 Non-Linear Filtering with Wiener Noise
- 13 The Conditional Density
- 14 Non-Linear Filtering with Counting-Process Observations
- 15 Filtering with k-Variate Counting-Process Observations
- Part V Applications in Financial Economics
- References
- Index of Symbols
- Subject Index
Summary
Here we derive the basic filtering theory for processes with scalar counting-process observations. We discuss optional and predictable projections, introduce the innovation process, and derive the non-linear filtering equations. We also derive the filtering equations for a finite-state Markov chain. We prove a result concerning separation between filtering and detection and we derive the relevant Zakai equation for the unnormalized density.
Keywords
- Type
- Chapter
- Information
- Point Processes and Jump DiffusionsAn Introduction with Finance Applications, pp. 149 - 162Publisher: Cambridge University PressPrint publication year: 2021