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
43 pages build on this one.
- Kolmogorov backward equation
- Martingale representation theorem
- Itô's lemma
- Polar sets and Brownian hitting
- Stochastic partial differential equation
- Stochastic Volterra equation
- Itô isometry
- Stratonovich integral
- Rough path
- Stochastic optimal control
- Variogram
- Donsker's theorem
- Fokker–Planck equation
- Excessive function
- Milstein method
- Potential operator of a Markov process
- Local time
- Kakutani's solution of the Dirichlet problem
- Random ordinary differential equation
- Euler–Maruyama method
- Linear-quadratic-Gaussian control
- Doob's h-transform
- Green's function of a Markov process
- Quasi-invariant measure
- Malliavin calculus
- Tanaka's formula
- Conditioned Brownian motion
- Diffusion process
- Hunt process
- Runge–Kutta method for stochastic differential equations
- Dickey–Fuller test
- Itô calculus
- Doléans-Dade exponential
- Langevin equation
- Separation principle
- Kolmogorov continuity theorem
- Feynman–Kac formula
- Cameron–Martin theorem
- Harmonic measure as exit distribution
- 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 |
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Used by
- Kolmogorov backward equation
- Martingale representation theorem
- Itô's lemma
- Polar sets and Brownian hitting
- Stochastic partial differential equation
- Stochastic Volterra equation
- Itô isometry
- Stratonovich integral
- Rough path
- Stochastic optimal control
- Variogram
- Donsker's theorem
- Fokker–Planck equation
- Excessive function
- Milstein method
- Potential operator of a Markov process
- Local time
- Kakutani's solution of the Dirichlet problem
- Random ordinary differential equation
- Euler–Maruyama method
- Linear-quadratic-Gaussian control
- Doob's h-transform
- Green's function of a Markov process
- Malliavin calculus
- Tanaka's formula
- Conditioned Brownian motion
- Diffusion process
- Hunt process
- Runge–Kutta method for stochastic differential equations
- Dickey–Fuller test
- Itô calculus
- Doléans-Dade exponential
- Langevin equation
- Kolmogorov continuity theorem
- Feynman–Kac formula
- Cameron–Martin theorem
- Harmonic measure as exit distribution
- Skorokhod's embedding theorem
- Schramm–Loewner evolution
- Stochastic differential equation
- Girsanov theorem
Results about this
- Polar sets and Brownian hitting
- Donsker's theorem
- Lévy's characterization of Brownian motion
- Kakutani's solution of the Dirichlet problem
- Reflection principle
- Harmonic measure as exit distribution
- Skorokhod's embedding theorem
- Girsanov theorem