Results 1 to 2 of 2

Math Help - Ito integral

  1. #1
    Newbie
    Joined
    Apr 2011
    Posts
    3

    Ito integral

    Well... I have a problem with Ito integral \int_{a}^{b} x(t)dw(t) , where x(t) is a stochasic process, and w(t) is Brownian motion (or Wiener process ). It is said that Ito integral cannot be considered as a Riemann-Stjelties integral because dW has no bounded variation. So for example let us consider sequence of approximating sums \sum _{i=1} ^{n} (x(t') w(t_{i} - t_{i-1})) where t' \in [t_{i-1}, t_{i}] and a=t_{0}<...<t_{n} =b is a division of integral [a,b]. In this case value of this integral does depend of choise of t'! And I've read that this is because Wiener process has no bounded variation.
    So my question is... why is this variation very important?
    I know how Wiener process look like and know its properties. But I just can't imagine why variation of it has this significant result in choise intermediate points t' ??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2011
    Posts
    3
    Hi! If there is anyone who knows anything about Brownian motion, stochastic ito integral, differential stochastic equation, please PLEASE write to me on priv because I have some ideas, and I consider about it, and I want to talk about it with someone.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 31st 2010, 08:38 AM
  2. Replies: 1
    Last Post: June 2nd 2010, 03:25 AM
  3. Replies: 0
    Last Post: May 9th 2010, 02:52 PM
  4. [SOLVED] Line integral, Cauchy's integral formula
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: September 16th 2009, 12:50 PM
  5. Replies: 0
    Last Post: September 10th 2008, 08:53 PM

Search Tags


/mathhelpforum @mathhelpforum