Difference between arithmetic vs geometric random walk

Question

I have read about arithmetic and geometric random walks. What is the difference between them?

Take an arithmetic random walk. Exponentiate it. That's a geometric random walk. However, be careful, because some authors mean something quite different by the term geometric random walk (one example, assuming my quick glance didn't miss something important, is here) — Glen_b, Dec 13 '13 at 03:04

score 7 · Accepted Answer · edited Dec 13 '13 at 09:55

Arithmetic random walks are modeled as sums of random terms while geometric random walks are modeled as products of random factors.

Two examples are Brownian Motion and Geometric Brownian Motion. Brownian Motion has independent, identically distributed increments while the geometric version has independent, identically distributed ratios between successive factors.

Difference between arithmetic vs geometric random walk

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