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The Oxford Handbook of Nonlinear Filtering (Hardcover)
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The Oxford Handbook of Nonlinear Filtering (Hardcover)
Series: Oxford Handbooks
Expected to ship within 12 - 19 working days
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In many areas of human endeavor, the systems involved are not
available for direct measurement. Instead, by combining
mathematical models for a system's evolution with partial
observations of its evolving state, we can make reasonable
inferences about it. The increasing complexity of the modern world
makes this analysis and synthesis of high-volume data an essential
feature in many real-world problems.
The celebrated Kalman-Bucy filter, designed for linear dynamical
systems with linearly structured measurements, is the most famous
Bayesian filter. Its generalizations to nonlinear systems and/or
observations are collectively referred to as nonlinear filtering
(NLF), an extension of the Bayesian framework to the estimation,
prediction, and interpolation of nonlinear stochastic dynamics. NLF
uses a stochastic model to make inferences about an evolving system
and is a theoretically optimal algorithm.
The breadth of its applications, firmly established and still
emerging, is simply astounding. Early uses such as cryptography,
tracking, and guidance were mostly of a military nature. Since
then, the scope has exploded. It includes the study of global
climate, estimating the state of the economy, identifying tumors
using non-invasive methods, and much more.
The Oxford Handbook of Nonlinear Filtering is the first
comprehensive written resource for the subject. It contains
classical and recent results and applications, with contributions
from 58 authors. Collated into 10 parts, it covers the foundations
of nonlinear filtering, connections to stochastic partial
differential equations, stability and asymptotic analysis,
estimation and control, approximation theory and numerical methods
for solving the nonlinear filtering problem (including particle
methods). It also contains a part dedicated to the application of
nonlinear filtering to several problems in mathematical finance.
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