In this numerical project, we observe Corollaries 3.16 and 3.17 in action. Consider n = 1,...,...

 

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In this numerical project, we observe Corollaries 3.16 and 3.17 in action. Consider n = 1,..., 20. For each n, consider the dyadic partition of [0,1] given by t;= j/2". Sample a single Brownian path with time step 2-20 on [0, 1]. For this single path: (a) Compute for each n the variation 2"-1 (+1 - |- j=0 (b) Compute for each n the quadratic variation 2n-1 (Btj+1 - Bt,). j=0 (c) Draw the graph of the variation and of the quadratic variation as a function of n, n = 1,..., 20. What do you observe? In this numerical project, we observe Corollaries 3.16 and 3.17 in action. Consider n = 1,..., 20. For each n, consider the dyadic partition of [0,1] given by t;= j/2". Sample a single Brownian path with time step 2-20 on [0, 1]. For this single path: (a) Compute for each n the variation 2"-1 (+1 - |- j=0 (b) Compute for each n the quadratic variation 2n-1 (Btj+1 - Bt,). j=0 (c) Draw the graph of the variation and of the quadratic variation as a function of n, n = 1,..., 20. What do you observe?