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Problems and Solutions in Mathematical Finance: Stochastic Calculus, Volume I by Eric Chin, Sverrir Olafsson, Dian Nel

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2.2.2 Markov Property

  1. 1. The Markov Property of a Standard Wiener Process. Let c02-math-340 be a probability space and let c02-math-341 be a standard Wiener process with respect to the filtration c02-math-342, c02-math-343. Show that if c02-math-344 is a continuous function then there exists another continuous function c02-math-345 such that
    equation

    for c02-math-346.

    Solution

    For c02-math-347 we can write

    equation

    Since c02-math-348 and is measurable, by setting where is a constant value

    Because we can write

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