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A decomposition of the Brownian path

✍ Scribed by Ioannis Karatzas; Steven E. Shreve

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 308 KB
Volume: 5
Category: Article
ISSN: 0167-7152
DOI: 10.1016/0167-7152(87)90061-7

No coin nor oath required. For personal study only.

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Let G be a loopless finite multigraph. For each vertex x of G, denote its degree and multiplicity by d(x) and p(x) respectively. Define the least even integer 2 p(x), if d(x) is even, the least odd integer 2 p(x), if d(x) is odd. In this paper it is shown that every multigraph G admits a faithful p