I am trying to learn about stochastic calculus for my research, so self study, and I came across the notion of a Standard Brownian Filtration. I cannot find a good definition of what the Standard Brownian Filtration is, and I was wondering if anyone had a good definition or a link to one. I do not think they define it in the book I am reading and I cannot find a definition online easily.
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Maybe the natural filtration of a standard brownian motion. – Augustin Aug 22 '15 at 19:51
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By this you mean the filtration that a Brownian Motion is over? – MathStudent Aug 22 '15 at 19:57
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1I mean the filtration defined by $\mathcal{F}_t=\sigma(W_s\colon s\leq t)$ – Augustin Aug 22 '15 at 19:59
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What is the definition of that? – MathStudent Aug 22 '15 at 20:15
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Never mind, I understand now. Thank you – MathStudent Aug 22 '15 at 20:18
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$\mathcal{F}t$ is the $\sigma$-algebra generated by the family of random variables $(W_s){s\leq t}$, where $W$ is your brownian motion. – Augustin Aug 22 '15 at 20:19