Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Use Theorem 12.5 to show that (kappa(t)=(1+epsilon) sqrt{2 t log

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Let $\left(B_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{1}$. Use Theorem 12.5 to show that $\kappa(t)=(1+\epsilon) \sqrt{2 t \log |\log t|}$ is an upper function for $t ightarrow 0$.

Data From Theorem 12.5

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Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

ISBN: 9783110741254

3rd Edition

Authors: René L. Schilling, Björn Böttcher

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Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Use Theorem 12.5 to show that (kappa(t)=(1+epsilon) sqrt{2 t log

Question:

12.5 Theorem (Kolmogorov's test). Let (Br)o be a BM and x: (0,1] (0,00) continuous function such that x(t) is increasing and x(t)/f is decreasing. Then the following alternative holds: Ex. 12.4 Ex. 12.5 x(t) exp(-) dt 1)=1. B(t) x(t) XI 1) = 1. (12.7)

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Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

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