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Brownian Motion, 2nd Edition by Björn Böttcher, Lothar Partzsch, René L. Schilling

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A Appendix

A.1 Kolmogorov’s existence theorem

In this appendix we give a proof of Kolmogorov’s theorem, Theorem 4.8, on the existence of stochastic processes with prescribed finite dimensional distributions. In addition to the notation introduced in Chapter 4, we use e9783110307290_i5066.jpg for the projection onto the coordinates from J ⊂ L ⊂ I. Moreover, e9783110307290_i5067.jpgand we write ℌ for the family of all finite subsets of I. Finally

e9783110307290_i5068.jpg

denotes the family of cylinder sets and we call ...

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