Results 1 to 2 of 2

Math Help - Variance and mean of a deterministic process

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    28

    Variance and mean of a deterministic process

    Let (f_t)_{t \geq 0} be a deterministic process (i.e. independent of \omega) such that \int_{0}^{\infty }\int_{t}^{2}dt<\infty. Then this process obviously belongs to H. Show that for each t the integral \int_{0}^{t}f_sdW_s is a normal random variable with mean 0 and variance \int_{0}^{t}f_s^2ds

    Any help?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6

    Re: Variance and mean of a deterministic process

    Hello,

    Use the basic properties of a stochastic integral!
    The expectation of a stochastic integral is proved to be 0 (by using the core definition, dealing with sum of brownian increments).
    The variance is obtained by Ito's isometry.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Deterministic Objecive Function
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: March 18th 2012, 01:52 PM
  2. Variance of a t-realization of a stochastic process
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: December 17th 2011, 11:59 PM
  3. Variance of a branching process
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 11th 2011, 09:52 AM
  4. Calculating Variance - Poisson process
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 24th 2011, 03:13 PM
  5. Variance in poisson process
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 23rd 2010, 08:02 PM

Search Tags


/mathhelpforum @mathhelpforum