Brownian Motion
Wiener process, sample-path regularity, and martingale characterization.
Brownian Motion. Wiener process, sample-path regularity, and martingale characterization.
Foundations and canonical references
The standard treatments of brownian motion approach the subject from complementary angles. Karatzas, Brownian Motion and Stochastic Calculus (1991) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Revuz, Continuous Martingales and Brownian Motion (1999) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for brownian motion include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1991Brownian Motion and Stochastic Calculuskaratzas-1991, shreve-1991
- textbook · primary · 1999Continuous Martingales and Brownian Motionrevuz-1999, yor-1999
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