Asymptotic Ergodicity of the Process of Conditional Law in Some Problem of Non-linear Filtering

✍ Scribed by Giuseppe Da Prato; Marco Fuhrman; Paul Malliavin

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 171 KB
• Volume: 164
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1999.3399

✦ Synopsis

We consider a sample of a trajectory of an ergodic process m x through a stationary noisy observation process. We study the asymptotic ergodicity of the phase process.

1999 Academic Press

Contents.

1. Meaning of asymptotic ergodicity. 2. Robust resolution of the Zakai equation through a phase transform. 3. Representation of q t through a Girsanov formula. 4. Estimation of logarithmic derivatives by the stochastic calculus of variations. 5. Asymptotic ergodicity of the phase process. 6. Vanishing of the remote past. 7. Asymptotic ergodicity. Appendix: Minoration of the fundamental solution of a Ho rmander type operator.

1. MEANING OF ASYMPTOTIC ERGODICITY

An ergodic process m x is given and a sample of its trajectory is fixed. This sample is observed through a stationary noisy observation process. What is the amount of information that the non-linear filtering algorithm can bring when the observation time becomes large?