Abstract
The importance of reproducing kernel Hilbert spaces in the study of Gaussian processes is illustrated in two concrete problems. The first deals with mutual singularity of the law of the solution of a stochastic partial differential equation and the law of the driving process. The second gives a characterization for a Gaussian process to be a semimartingale in terms of reproducing kernel Hilbert spaces. Expansion of filtrations for Gaussian processes is discussed.
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Koski, T., Sundar, P. (2001). Two Applications of Reproducing Kernel Hilbert Spaces in Stochastic Analysis. In: Hida, T., Karandikar, R.L., Kunita, H., Rajput, B.S., Watanabe, S., Xiong, J. (eds) Stochastics in Finite and Infinite Dimensions. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0167-0_11
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DOI: https://doi.org/10.1007/978-1-4612-0167-0_11
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