Probability theory and stochastic processes Brownian motion Concept
Wiener process
Summary
The Wiener process, or standard Brownian motion, is the continuous-time stochastic process with continuous paths and independent, normally distributed increments. It is the scaling limit of random walks and the basic model of random motion. It is a Gaussian process, a Lévy process, a martingale and a Markov process at the same time.
Where this leads
23 pages build on this one.
- Kolmogorov backward equation
- Martingale representation theorem
- Itô's lemma
- Itô isometry
- Stratonovich integral
- Rough path
- Donsker's theorem
- Local time
- Random ordinary differential equation
- Euler–Maruyama method
- Quasi-invariant measure
- Malliavin calculus
- Tanaka's formula
- Diffusion process
- Itô calculus
- Doléans-Dade exponential
- Langevin equation
- Kolmogorov continuity theorem
- Cameron–Martin theorem
- Skorokhod's embedding theorem
- Schramm–Loewner evolution
- Stochastic differential equation
- Girsanov theorem
Further reading
About this page
| Tag | 22735FGJV6 |
|---|---|
| URI | m2://22735FGJV6 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 60J65, 60G15 |
| Specializes | Gaussian process, Lévy process |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Kolmogorov backward equation
- Martingale representation theorem
- Itô's lemma
- Itô isometry
- Stratonovich integral
- Rough path
- Donsker's theorem
- Local time
- Random ordinary differential equation
- Euler–Maruyama method
- Malliavin calculus
- Tanaka's formula
- Diffusion process
- Itô calculus
- Doléans-Dade exponential
- Langevin equation
- Kolmogorov continuity theorem
- Cameron–Martin theorem
- Skorokhod's embedding theorem
- Schramm–Loewner evolution
- Stochastic differential equation
- Girsanov theorem