Abstract
As was announced in §1.3, (ii), this chapter is devoted to a study of the distributions of generalised stochastic processes. In the finite-dimensional case Bochner’s theorem establishes a one-to-one correspondence between distributions and characteristic functions, and this result has a counterpart in the present context, where the Bochner-Minlos theorem (§3.2) links probability measures on the space of generalised functions with characteristic functionals on the space of test functions. A secondary aim of this chapter is to provide a discussion of the generalised stochastic process white noise from several points of view (§§3.3, 3.4), this serving as background to much of what will be considered in the next chapter.
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© 1980 Takeyuki Hida
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Hida, T. (1980). Generalised Stochastic Processes and Their Distributions. In: Brownian Motion. Applications of Mathematics, vol 11. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6030-1_3
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DOI: https://doi.org/10.1007/978-1-4612-6030-1_3
Publisher Name: Springer, New York, NY
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