Abstract
The necessary and sufficient conditions are given so that a non-anticipative transformation in Hilbert space is isometric. In terms of second order Wiener process, these conditions assure that a non-anticipative transformation of Wiener process is a Wiener process, too.
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Ivković, Z., Pantić, D. Linear Isometric Non-Anticipative Transformations of Wiener Process. Chin. Ann. of Math. 21, 109–114 (2000). https://doi.org/10.1007/BF02731964
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DOI: https://doi.org/10.1007/BF02731964
Keywords
- Resolution of identity
- Separable Hilbert space
- Wide sense Wiener process
- Non-anticipative transformation