Reference for the Construction of Brownian Motion

Question

A common method for constructing Brownian motion is referred to as the Levy construction, the Levy-Ciesielski construction, the Ciesielski construction and sometimes seems to be attributed to Wiener (1923). At least in the book, Diffusions, Markov Processes and Martingales by Rogers and Williams, I can find a reference for Ciesielski:

@article{Ciesielski61,
 author = {Z. Ciesielski},
 title = {Holder condition for realization of {G}aussian processes},
 journal = tams,
 volume={99},
 year = 1961,
 pages={403--413}
}

Can someone point me at the references for Levy and Wiener? Or perhaps even better there is an article with a short history of the construction of Brownian motion?

Answer 1

The monograph Brownian Motion - An Introduction to Stochastic Processes by René Schilling & Lothar Partzsch contains (proofs of) the following constructions of Brownian motion:

• Lévy-Cieselski construction
• Wiener's construction
• Lévy's construction
• construction via orthogonal series
• (sketch of) Donsker's construction
• construction via Kolmogorov's existence theorem

Answer 2

The reference for Lévy is:

Lévy, M. Paul. “Le Mouvement Brownien Plan.” American Journal of Mathematics, vol. 62, no. 1, 1940, pp. 487–550. JSTOR, www.jstor.org/stable/2371467. Accessed 24 Nov. 2020.