This paper is concerned with continuous-time nonlinear risk-sensitive filters. It is shown that for large classes of nonlinearities entering both the dynamics and measurements, these filters are finitedimensional generalizations of the Benes filters. Specific examples are discussed. The small noise limiting analog is discussed using change of probability measures. Publisher Item Identifier S 0018-9286(98)06601-X. the scalar product in < n . xt is the state of the system at time t, which is not

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... irectly measurable. Rather, the only information available for x t is through the observations process fys ; 0 s t < Tg. Unlike the minimum variance estimation problem which minimizes the expected value of the square of the error at time t given fy s ; 0 s tg, the problem to be discussed here is the so-called risk-sensitive estimation problem. This aims to minimize the expected value of an exponentialof-integral of the error, given the past and present measurements 0018-9286/98$10.00