# Robust Approximation in a Filtering Problem with Real State Space and Counting Observations

Robust Approximation in a Filtering Problem with Real State Space and Counting Observations Let (X t ,Y t ) be a pure jump Markov process, where X t takes values in \bf R and Y t is a counting process. We compare the filter of this system and a filter of a suitably modified system. We compute an explicit bound for the distance in the so-called bounded Lipschitz metric between the two filters. Finally we show how to use this bound to construct a discrete space approximation of the filter. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Robust Approximation in a Filtering Problem with Real State Space and Counting Observations

, Volume 42 (1) – Jan 1, 2000
21 pages

/lp/springer_journal/robust-approximation-in-a-filtering-problem-with-real-state-space-and-xdC068YZ20
Publisher
Springer-Verlag
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002450010002
Publisher site
See Article on Publisher Site

### Abstract

Let (X t ,Y t ) be a pure jump Markov process, where X t takes values in \bf R and Y t is a counting process. We compare the filter of this system and a filter of a suitably modified system. We compute an explicit bound for the distance in the so-called bounded Lipschitz metric between the two filters. Finally we show how to use this bound to construct a discrete space approximation of the filter.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 1, 2000

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations