000 03769nam a22005055i 4500
001 978-3-0346-0176-4
003 DE-He213
005 20140220084518.0
007 cr nn 008mamaa
008 101127s2010 sz | s |||| 0|eng d
020 _a9783034601764
_9978-3-0346-0176-4
024 7 _a10.1007/978-3-0346-0176-4
_2doi
050 4 _aQA614-614.97
072 7 _aPBKS
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a514.74
_223
100 1 _aElworthy, K. David.
_eauthor.
245 1 4 _aThe Geometry of Filtering
_h[electronic resource] /
_cby K. David Elworthy, Yves Le Jan, Xue-Mei Li.
264 1 _aBasel :
_bSpringer Basel,
_c2010.
300 _aXI, 169p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aFrontiers in Mathematics,
_x1660-8046
505 0 _aDiffusion Operators -- Decomposition of Diffusion Operators -- Equivariant Diffusions on Principal Bundles -- Projectible Diffusion Processes and Markovian Filtering -- Filtering with non-Markovian Observations -- The Commutation Property -- Example: Riemannian Submersions and Symmetric Spaces -- Example: Stochastic Flows -- Appendices.
520 _aThe geometry which is the topic of this book is that determined by a map of one space N onto another, M, mapping a diffusion process, or operator, on N to one on M. Filtering theory is the science of obtaining or estimating information about a system from partial and possibly flawed observations of it. The system itself may be random, and the flaws in the observations can be caused by additional noise. In this volume the randomness and noises will be of Gaussian white noise type so that the system can be modelled by a diffusion process; that is it evolves continuously in time in a Markovian way, the future evolution depending only on the present situation. This is the standard situation of systems governed by Ito type stochastic differential equations. The state space will be the smooth manifold, N, possibly infinite dimensional, and the "observations" will be obtained by a smooth map onto another manifold, N, say. We emphasise that the geometry is important even when both manifolds are Euclidean spaces. This can also be viewed from a purely partial differential equations viewpoint as one smooth second order elliptic partial differential operator lying above another, both with no zero order term. We consider the geometry of this situation with special emphasis on situations of geometric, stochastic analytic, or filtering interest. The most well studied case is of one Brownian motion being mapped to another with a consequent skew product decomposition (or equivalently the case of Riemannian submersions). This sort of decomposition is generalised and a key to the rest of the book. It is used to study in particular, classical filtering, (semi-)connections determined by stochastic flows, and generalised Weitzenbock formulae.
650 0 _aMathematics.
650 0 _aGlobal analysis.
650 0 _aGlobal differential geometry.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
650 2 4 _aDifferential Geometry.
650 2 4 _aProbability Theory and Stochastic Processes.
700 1 _aLe Jan, Yves.
_eauthor.
700 1 _aLi, Xue-Mei.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034601757
830 0 _aFrontiers in Mathematics,
_x1660-8046
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0346-0176-4
912 _aZDB-2-SMA
999 _c111092
_d111092