Advances on Theoretical and Methodological Aspects of by N. Balakrishnan

By N. Balakrishnan

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2 we then have that πtX is a solution to the martingale problem corresponding to (A0, η). We now show that it is the unique solution. 10). Then the martingale problem for (A0, η) is well posed. e. 13) and Z0=η. 3). 3) we will have that the distribution of Zt is the same as that of πtX, proving the well-posedness of the martingale problem for (A0, η). 16) . Let ∆=∆(F, g) be a bound for Now suppose the integral . Suppose is a function [Hirsch (1976, pp. 41–42)] such that Suppose , so that and f(x)=x, for |x|Յ∆.

The signal or system process , is unobservable. Information about (Xt) is obtained by observing another process Y which is a function of X corrupted by noise. 1) where h is a measurable function and (Wt) is a standard Wiener process. MANDAL information about Xt. The primary aim of filtering theory is to get an estimate of Xt based on the information . This is given by the conditional distribution vt of Xt given , or equivalently, the conditional expectation for a rich enough class of functions f.

Characterization of the optimal filter: The non Markov case, Preprint. B. (1965). Markov Processes, Vols. I, II, Springer-Verlag, Berlin. N. G. (1986). Markov Processes: Characterization and Convergence, John Wiley & Sons, New York. , Kallianpur, G. and Kunita, H. (1972). Stochastic differential equations for the nonlinear filtering problem, Osaka Journal of Mathematics, 9, 19–40. W. (1976). Differential Topology, Springer-Verlag, New York. Horowitz, J. L. (1990). ), pp. 75–122, Birkhaüser, Boston.

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