# Counting Observations: A Note on State Estimation Sensitivity with an L 1 -Bound

Counting Observations: A Note on State Estimation Sensitivity with an L 1 -Bound Let (X t , Y t ) be a pure jump Markov process: the state X t takes real values and the observation Y t is a counting process. The two processes are allowed to have common jump times. Let ϕ(X(⋅)) be a functional of the state trajectory restricted to the time interval [0, T] . If we change the infinitesimal parameters and/ or the initial distribution, then we introduce an error in computing the conditional law of ϕ(X(⋅)) given the observation up to time T . In this paper we give an explicit L 1 -bound for this error. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Counting Observations: A Note on State Estimation Sensitivity with an L 1 -Bound

, Volume 44 (2) – Jan 1, 2001
25 pages

/lp/springer_journal/counting-observations-a-note-on-state-estimation-sensitivity-with-an-l-RyS5cNnkl7
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/s00245-001-0018-6
Publisher site
See Article on Publisher Site

### Abstract

Let (X t , Y t ) be a pure jump Markov process: the state X t takes real values and the observation Y t is a counting process. The two processes are allowed to have common jump times. Let ϕ(X(⋅)) be a functional of the state trajectory restricted to the time interval [0, T] . If we change the infinitesimal parameters and/ or the initial distribution, then we introduce an error in computing the conditional law of ϕ(X(⋅)) given the observation up to time T . In this paper we give an explicit L 1 -bound for this error.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 1, 2001

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