/sci/ - Science & Math

>>10645460
WUBBA LUBBA DUB DUBBBBB
I'M HVAC RICCCCKKKKK

>>10319362
300k starting
any job i want

>>9362676
olympic weightlifting

mountain biking

classical piano

all highly technique-dependent activities that require intense concentration and can be done alone

they also promote physical fitness (first two) and posture/poise (third) which should be neglected by anyone doing intellectual work-your mind will work better if you keep your body in working order

>>9330638
mfw multiple beta orbitters offering to sit this girl through online tests in the library for a grad scheme

>Start with the year of your birth
>add your age
>if you haven't had your birthday yet this year, add one
>Answer is always 2017

What's the scientific explanation for this?

>>9273800
Like you say, it is defined as a Riemann-Stieltjes integral. However, the function W_s almost surely does not have bounded variation. It is known that for such functions, the RS integral cannot be defined. More precisely, given g not of BV, there exists a continuous f so that the integral [math] \int fdg[/math] diverges.

However, there is a theorem of Young that if f is holder continuous of degree a, and g is Holder continuous of degree b, then [math] \int fdg[/math] is well-defined, provided that a+b>1. If I recall correctly, the sample paths of Brownian motion are holder continuous of degree [math] 1/2-\epsilon[/math] for all [math] \epsilon>0[/math]. Thus the Riemann-Steljes sums do converge pointwise almost surely provided that X_s is almost surely Holder continuous with exponent [math] 1/2+\epsilon[/math] for some epsilon.