Abstract
Let (E, ℱ, P) be a probability space and (β(t), ℱ t , P) a d-dimensional Brownian motion. The purpose of this section is to point out some of the properties that (β(t), ℱ t , P) possesses in common with a much larger class of stochastic processes which we will be calling Itô processes. Since we are going to be giving a completely rigorous derivation of these properties in the more general context of Itô processes, our treatment here will be somewhat informal and proofs will not be complete.
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© 2006 Springer-Verlag Berlin Heidelberg
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Stroock, D.W., Varadhan, S.R.S. (2006). The Stochastic Calculus of Diffusion Theory. In: Multidimensional Diffusion Processes. Classics in Mathematics / Grundlehren der mathematischen Wissenschaften. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28999-2_5
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DOI: https://doi.org/10.1007/3-540-28999-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-22201-0
Online ISBN: 978-3-540-28999-9
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