Abstract
Having stated the problems we would like to solve, we now proceed to find reasonable mathematical notions corresponding to the quantities mentioned and mathematical models for the problems. In short, here is a first list of the notions that need a mathematical interpretation:
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(1)
A random quantity
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(2)
Independence
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(3)
Parametrized (discrete or continuous) families of random quantities
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(4)
What is meant by a “best” estimate in the filtering problem (Problem 3)
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(5)
What is meant by an estimate “based on” some observations (Problem 3)?
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(6)
What is the mathematical interpretation of the “noise” terms?
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(7)
What is the mathematical interpretation of the stochastic differential equations?
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© 1992 Springer-Verlag Berlin Heidelberg
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Øksendal, B. (1992). Some Mathematical Preliminaries. In: Stochastic Differential Equations. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02847-6_2
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DOI: https://doi.org/10.1007/978-3-662-02847-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53335-1
Online ISBN: 978-3-662-02847-6
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