Formalization of a Brownian motion and of stochastic integrals in Lean

Bibliography

Part 1 Bibliography

Hai09

Martin Hairer, An introduction to stochastic pdes, arXiv preprint arXiv:0907.4178 (2009).

KU23

Volker Krätschmer and Mikhail Urusov, A kolmogorov–chentsov type theorem on general metric spaces with applications to limit theorems for banach-valued processes, Journal of Theoretical Probability 36 (2023), no. 3, 1454–1486.

Tal22

Michel Talagrand, Upper and lower bounds for stochastic processes: decomposition theorems, vol. 60, Springer Nature, 2022.

Part 2 Bibliography

BSV12

Mathias Beiglböck, Walter Schachermayer, and Bezirgen Veliyev, A short proof of the doob–meyer theorem, Stochastic Processes and their Applications 122 (2012), no. 4, 1204–1209.

Kal21

Olav Kallenberg, Foundations of modern probability, third edition ed., Probability Theory and Stochastic Modelling, vol. 99, Springer Nature Switzerland, 2021.

Low

George Lowther, Almost sure - a random mathematical blog, Accessed: 2025-09-14.

Pas24

Andrea Pascucci, Probability theory ii: Stochastic calculus, UNITEXT, vol. 166, Springer Nature Switzerland, Cham, 2024 (en).