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Antonio F. Gualtierotti
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Antonio F. Gualtierotti: University of Lausanne, HEC and IDHEAP

Chapter Chapter 10 in Detection of Random Signals in Dependent Gaussian Noise, 2015, pp 795-850 from Springer

Abstract: Abstract This chapter covers two topics. As explained below, the “usual conditions” [70, p. 183] of stochastic calculus are not adequate in the present context. There is thus a section on sets of measure zero, enlargements of algebras using such sets, and restrictions to their complement. Exponentials of continuous martingales, continuous processes with independent increments, and the Wiener process are all closely related, and there is thus a second section in which those relations are examined, when the processes used take their values in l 2, the Hilbert space of sequences, whose components have squares that sum up to a finite number. The presence of l 2 is a consequence of the Cramér-Hida representation.

Keywords: Independent Increments; Stochastic Calculus; Local Martingale; Stopping Time; Uniform Boundedness Property (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22315-5_10

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DOI: 10.1007/978-3-319-22315-5_10

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