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Problem 6 (8 points) Determine directly from the definition of the Stratonovitch integral: Xt = Bt - s ? BsodB s . Jo Remark: Set

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Problem 6 (8 points) Determine directly from the definition of the Stratonovitch integral: Xt = Bt - s ? BsodB s . Jo Remark: Set up a family of elementary processes which approximates the integrand and show that it converges in L'-towards I(t). Observe that this does not imply a pathwise construction of the integral. What can be done to achieve a pathwise construction? Apply Kolmogorov's continuity condition to show that the process X has continuous sample paths almost surely. Is there another possibility to do so? Given the canonical filtration 5 := o{B,|0

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