Let (W(t): 0t T} denote a Brownian motion and {A(t): 0 tT} an adapted stochastic process....

 

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Let (W(t): 0≤t≤ T} denote a Brownian motion and {A(t): 0 ≤t≤T} an adapted stochastic process. Consider the Itô integral I(T) = A(t)dw (t). (i) Give the computational interpretation of I(T). (ii) Show that {I(t): 0 ≤t≤T} is a martingale. Let (W(t): 0≤t≤ T} denote a Brownian motion and {A(t): 0 ≤t≤T} an adapted stochastic process. Consider the Itô integral I(T) = A(t)dw (t). (i) Give the computational interpretation of I(T). (ii) Show that {I(t): 0 ≤t≤T} is a martingale.

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