My Math Forum Wiener integral - is it Cauchy sequence in L^2 ?

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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: $\displaystyle f(x)= \sum_{i=1}^{n}a_i I_{[t_{i-1}, t_i)}(x)$ Wiener integral: $\displaystyle I(f)= \sum_{i=1}^{n} a_i (B_{t_i}-B_{t_{i-1}})$ 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.

 Tags cauchy, integral, sequence, wiener

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