Asymptotic expansion for a filtering problem and a short term rate model.

Authors :: Anderson, Robert
Castaing, Charles
Clarke, Frank H.
Dierker, Egbert
Duffie, Darrell
Evans, Lawrence C.
Fujimoto, Takao
Grandmont, Jean-Michel
Hirano, Norimichi
Hurwicz, Leonid
Ichiishi, Tatsuro
Ioffe, Alexander
Iwamoto, Seiichi
Kamiya, Kazuya
Kawamata, Kunio
Kikuchi, Norio
Maruyama, Toru
Matano, Hiroshi
Nishimura, Kazuo
Richter, Marcel K.
Source :: Advances in Mathematical Economics (9784431343417); 2006, p33-48, 16p
Publication Year :: 2006
Abstract: We study the filtering problem in which a system process Xt(ε) and a observing process Yt(ε) depend on the parameter ε, and Xt(ε) converges to a deterministic function Xt(0) as ε ↓ 0. We give an asymptotic expansion formula in Lp for the conditional expectation of a function of Xt(ε) under the σ-field generated by the process Ys(ε), 0 ≤ s ≤ t. [ABSTRACT FROM AUTHOR]