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- W1665191623 abstract "An elementary construction of the Wiener process is discussed, based on a proper sequence of simple symmetric random walks that uniformly converge on bounded intervals, with probability 1. This method is a simplification of F.B. Knight's and P. R'ev'esz's. The same sequence is applied to give elementary (Lebesgue-type) definitions of It^o and Stratonovich sense stochastic integrals and to prove the basic It^o formula. The resulting approximating sums converge with probability 1. As a by-product, new elementary proofs are given for some properties of the Wiener process, like the almost sure non-differentiability of the sample-functions. The purpose of using elementary methods almost exclusively is twofold: first, to provide an introduction to these topics for a wide audience; second, to create an approach well-suited for generalization and for attacking otherwise hard problems." @default.
- W1665191623 created "2016-06-24" @default.
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- W1665191623 date "2010-08-09" @default.
- W1665191623 modified "2023-09-27" @default.
- W1665191623 title "An elementary introduction to the Wiener process and stochastic integrals" @default.
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