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- mushrooman
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limit of dWt/dt as t goes to 0
can someone shed some light on the limit of dWt/dt as t goes to 0, where Wt is a Brownian motion or a normal r.v with mean 0 and variance t.Thanks a lot in advance
limit of dWt/dt as t goes to 0
Hi Do you mean ?If so note that for a Brownian motion, in distribution...and so the limit goes to infinity in probability and the limsup goes to infinity almost surely...You may find a rigourous proof in some text book... look at the differetiability of the Brownian motion (non-differentiable).
limit of dWt/dt as t goes to 0
to add to what wheeb said, differentiability is generally proven as finding a number say M, so that as dt->0 abs(df/dt-M)<e where e is a some arbitrarily chosen small real number.but for f=w, it turns out there is no M, because dw=N(0,1)*sqrt(dt) and so dw/dt=N(0,1)/dt
limit of dWt/dt as t goes to 0
last 5-6 words of my last post shud be... and so dw/dt=N(0,1)/sqrt(dt)