Let be a Brownian motion. Show that the following processes are Brownian motions on [0,T].

1. .

2. where .

3. where .

4. and .

Who ever can answer all of these is legendary. Any help will be greatly appreciated. Thanks.

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- Jun 10th 2009, 01:24 AMsymmetry7Brownian motion
Let be a Brownian motion. Show that the following processes are Brownian motions on [0,T].

1. .

2. where .

3. where .

4. and .

Who ever can answer all of these is legendary. Any help will be greatly appreciated. Thanks. - Jun 10th 2009, 08:35 AMcl85
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.