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Titlebook: Applied Stochastic Analysis; Proceedings of a US- Ioannis Karatzas,Daniel Ocone Conference proceedings 1992 Springer-Verlag Berlin Heidelbe

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A nonlinear filter with two time scales,ndard Wiener process (.., ..), and the observation is given by ..=.... for an independent Wiener process .. and a small positive parameter ε. We describe a suboptimal filter and estimate its difference with the optimal one as ε → 0. It appears that the estimation of the two components of the signal involves two different time scales.
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https://doi.org/10.1007/978-1-4419-0840-7We use association properties satisfied by partial sums of the holding times in order to prove that the firing epochs compare for stochastic ordering with the last birth in a multitype branching process, the structure of which is determined from the characteristics of the event graph using simple al
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J. E. Butler,J. H. Peterman,T. E. Koertgeewise monotone with finitely many intervals of monotonicity. A sequential quadratic variation test is used to detect intervals of monotonicity of the observation function. It is shown that the original nonlinear model can be approximated by a simple linear model in the sense that the difference of t
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Enzyme Mediated Immunoassay: An Overview the drift of a Brownian motion under partial observations. The general case is worked out in [3]..The point of view we adopt is a combination of results of P. L. Lions on the control of the Zakai equation [4] and results of the author on the control of diffusions in finite dimensions [2].
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