Abstract
Having defined linear diffusions (cf. No. II.1), standard one-dimensional Brownian motion W = {Wt : t ≥ 0}can be defined as a linear diffusion on ℝ with the speed measure m(dx) = 2 dx and the scale function s(x) = x. This is equivalent to saying that the infinitesimal generator of W is the second order differential operator
acting on the domain \(D\left( g \right) = C_{b}^{2}\left( \mathbb{R} \right)\). For the basic data of W see No. A1.1.
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© 1996 Birkhäuser Verlag Basel
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Borodin, A.N., Salminen, P. (1996). Brownian Motion. In: Handbook of Brownian Motion — Facts and Formulae. Probability and Its Applications. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7652-0_4
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DOI: https://doi.org/10.1007/978-3-0348-7652-0_4
Publisher Name: Birkhäuser, Basel
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