Thursday, August 15, 2013

Stoch Lesson 15 - paths and time-varying random variables

See Lesson 05 for a backgrounder on the n steps of random walk...

RVRV is my own jargon, related to a stoch process. Before I'm confident to use the process jargon, I'll use my own jargon.

Every time-varying-random-variable has a "Level" [1] at a given time, and therefore the variable has paths. The concept of path and the concept of time-varying-random-variable are intertwined.

For the random walker to go though the n steps one round, we query the noisegen n times. That's a single realization of the random Process. If the walk is on a conveyer belt, then we see a "path". One realization maps to one path. 9999 realizations would show 9999 paths and produce a good histogram.

Not everything we see in the formulas is a TVRV. The "h" isn't; deltaAnything isn't; drift rate isn't ... W is, though deltaW (ΔW)  isn't. S is, though deltaS (ΔS) isn't.

A note on randomness assumed in a stoch process -- the future is usually assumed uncertain, but I won't conclude that anything and everything in the future is random. The maturity value of a 12M time deposit is known, since default risk is assumed zero.

[1] actually not a single Level but multiple possible Levels. At a given time on each possible path, there's a single Level.

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