On a multiplicative functional transformation arising in nonlinear filtering theory |
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Authors: | M H A Davis |
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Institution: | (1) Department of Electrical Engineering, Imperial College, SW7 2BT London, England |
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Abstract: | Summary This paper concerns the nonlinear filtering problem of calculating estimates Ef(xt)¦y s, s t] where {x
t} is a Markov process with infinitesimal generator A and {y
t} is an observation process given by dy
t=h(xt)dt +dwtwhere {w
t} is a Brownian motion. If h(xt) is a semimartingale then an unnormalized version of this estimate can be expressed in terms of a semigroup T
s,t
y
obtained by a certain y-dependent multiplicative functional transformation of the signal process {x
t}. The objective of this paper is to investigate this transformation and in particular to show that under very general conditions its extended generator is A
t
y
f=ey(t)h(A– 1/2h2)(e–y(t)h
f).Work partially supported by the U.S. Department of Energy (Contract ET-76-C-01-2295) at the Massachusetts Institute of Technology |
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Keywords: | |
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