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May 30th, 2015, 11:15 PM  #1 
Newbie Joined: May 2015 From: Poland Posts: 1 Thanks: 0  Wiener integral  is it Cauchy sequence in L^2 ?
$\displaystyle f \in L^2([0, \infty)) $ , $\displaystyle (f_n)_{n \ge 1 }$  sequence of step functions , $\displaystyle f_n \rightarrow f $ in $\displaystyle L^2([0, \infty)) $ definition of a step function: $\displaystyle f(x)= \sum_{i=1}^{n}a_i I_{[t_{i1}, t_i)}(x) $ Wiener integral: $\displaystyle I(f)= \sum_{i=1}^{n} a_i (B_{t_i}B_{t_{i1}})$ How to prove that $\displaystyle (I(f_n))_{n \ge 1}$ is Cauchy in $\displaystyle L^2 (\Omega, F, P)$ ? Last edited by natalia0302; May 30th, 2015 at 11:26 PM. 

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cauchy, integral, sequence, wiener 
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