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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 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post kaybees17 Real Analysis 1 October 22nd, 2013 12:48 PM alejandrofigueroa Real Analysis 4 October 20th, 2013 05:01 PM xdeimos Real Analysis 1 October 11th, 2013 10:29 PM jrklx250s Real Analysis 5 December 12th, 2011 06:20 PM babyRudin Real Analysis 6 October 10th, 2008 11:11 AM

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