Advances in Mathematical Economics, Volume 9 (Advances in by S. Kusuoka, A. Yamazaki

By S. Kusuoka, A. Yamazaki

Loads of fiscal difficulties can formulated as restricted optimizations and equilibration in their recommendations. a number of mathematical theories were delivering economists with essential machineries for those difficulties bobbing up in fiscal idea. Conversely, mathematicians were motivated by means of a number of mathematical problems raised by means of fiscal theories. The sequence is designed to compile these mathematicians who have been heavily attracted to getting new hard stimuli from fiscal theories with these economists who're looking for powerful mathematical instruments for his or her researchers.

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Stochastic differential equations for the non linear filtering problem. Osaka J. Math. : The filtering problem for affine term structure model of the bond, in Japanese. , Striebel, C : Estimation of stochastic processes, arbitrary system process with additive white noise observation errors. Ann. Math. Statist. : Stochastic filtering: A part of stochastic nonlinear analysis. : Asset pricing with stochastic volatility. Appl. Math. Optim. : Asymptotic behavior of the nonlinear filtering errors of Markov processes.

In this paper we define the rank statistics Rt^r of a stochastic process Xt by ( ^ ) / Q lxs

Xi''^)]\ ^^0 L*GT I ^ *• k=o -" for any p > 1 and n € N. There exist Ao{t), A2{t), Bo{t) and B2{t) such that lim sup lim sup j^{A{e,t)-Ao{t)-s^A2it)}\=0 \{Bi£,t)-Bo{t)-e^B2it)}\=0 for any p > 1 and n G N. b Ao(i) at b b^ A2(f) = § { e " ' " * - 4a 0, p € (1, oo) and n G N . We have = 0 Asymptotic expansion for afilteringproblem and a short term rate model Jo 47 Jo where we mean / Fi (s) dys = Fi {t)yt Vs dFi (s).

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