Stoch Lesson 59 meaning of q[=] in a simple SDE

See Lesson 55 about details on deltaW and dW
See Lesson 19 about N@T
See Lesson 33 for a backgrounder on the canonical Wiener variable W

The Hull definition of the canonical Wiener process (Lesson 33) —

deltaW = epsilon * sqrt(deltaT) // in discrete time
dW      = epsilon * sqrt(dT) // in continuous time

The “=” has a different meaning than in algebra.

Discrete time is simpler to understand. Recall deltaW is a stepsize of a random variable. The “=” doesn’t mean a step size value of 0.012 is equal to the product of an epsilon value and sqrt(deltaT).

The “=” means equivalent-to.

Here epsilon represents … (hold your breath)… a noisegen, in fact the canonical Gaussian noisegen.

I’d say both deltaW and epsilon are N@T. These are not regular variables.

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