Let be a Brownian motion. Show that the following processes are Brownian motions on [0,T].
2. where .
3. where .
4. and .
Who ever can answer all of these is legendary. Any help will be greatly appreciated. Thanks.
All your questions regarding Brownian motions is simply a matter of applying and checking the definition.
Definition of Brownian motion:
A continuous random process X(t) is a (standard) Brownian motion if it satisfies
- X(0) = 0
- Independent increments
- Increments are normally distributed with mean zero and variance equal to the time increment.