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- W150251142 abstract "Given a nice topological space Q (for example, a several-dimensional differentiable manifold), let ∞ be an extra point which is either isolated or the one-point compactification of Q according as Q is compact or not, let C∞(Q) be the space of bounded continuous functions f: Q ⋃ ∞ → R1 with f(∞) ≡ 0 , introduce the (continuous) sample paths w:t → x(t) ∈ Q ⋃ ∞ with x(t)∈Q (t + ∞) and x(+∞) ≡ ∞, define Markov times m, shifted paths w m + , and Borel algebras B and Bm+ as usual, take probabilities Pa(B) (a ∈Q⋃∞, B ∈ B) with the usual properties including P∞ [x(t) ≡ ∞ (t z 0)] = 1, and call the associated motion a diffusion if it starts afresh at each Markov time, i.e., if1)Pα(wm+∈B∣Bm+)=Pb(B) a∈Q,B∈B,b=x(m),m +∞ for each Markov time m and if, in addition, it is smooth, i.e., if the Green operators({G_alpha }:f to E.left[ {intlimits_0^{ + infty } {{e^{ - alpha t}}fdt} } right])map C ∞ (Q) into itself:2)GαC∞⊂C∞ α 01) and 2) are not Unrelated." @default.
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- W150251142 date "1996-01-01" @default.
- W150251142 modified "2023-09-27" @default.
- W150251142 title "Brownian motion in several dimensions" @default.
- W150251142 doi "https://doi.org/10.1007/978-3-642-62025-6_8" @default.
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