Suppose Mo, M,..., MN is a martingale, and let A0, A, AN-1 be an adapted stochas-...

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Suppose Mo, M₁,..., MN is a martingale, and let A0, A₁, AN-1 be an adapted stochas- tic process. Define the discrete-time stochastic integral (sometimes called a martingale transform) Io, 1,, IN by setting Io = 0 and n-1 In = Aj(Mj+1-M₁), n = 1,..., N. j=1 Show that Io, 11,..., IN is a martingale. Suppose Mo, M₁,..., MN is a martingale, and let A0, A₁, AN-1 be an adapted stochas- tic process. Define the discrete-time stochastic integral (sometimes called a martingale transform) Io, 1,, IN by setting Io = 0 and n-1 In = Aj(Mj+1-M₁), n = 1,..., N. j=1 Show that Io, 11,..., IN is a martingale.

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We have In1 In Ann1 Mn Also In An and M are Fm... View the full answer