An elementary introduction to the Wiener process and stochastic integrals

Details An elementary introduction to the Wiener process and stochastic integrals An elementary introduction to the Wiener process and stochastic integrals

2010-08-09

arxiv.org/abs/1008.1510v1

Studia Scientiarum Mathematicarum Hungarica, 31, 249-297 (1996)

Mathematics

Probability

45 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

An elementary introduction to the Wiener process and stochastic integrals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An elementary introduction to the Wiener process and stochastic integrals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An elementary introduction to the Wiener process and stochastic integrals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-83813