In stochastic calculus, stochastic logarithm of a semimartingale Y {\displaystyle Y} such that Y ≠ 0 {\displaystyle Y\neq 0} and Y − ≠ 0 {\displaystyle Y_{-}\neq 0} is the semimartingale X {\displaystyle X} given by d X t = d Y t Y t − , X 0 = 0. {\displaystyle dX_{t}={\frac {dY_{t}}{Y_{t-}}},\quad X_{0}=0.} In layperson's terms, stochastic logarithm of Y {\displaystyle Y} measures the cumulative percentage change in Y {\displaystyle Y} .
In stochastic calculus, stochastic logarithm of a semimartingale Y {\displaystyle Y} such that Y ≠ 0 {\displaystyle Y\neq 0} and Y − ≠ 0 {\displaystyle Y_{-}\neq 0} is the semimartingale X {\displaystyle X} given by d X t = d Y t Y t − , X 0 = 0. {\displaystyle dX_{t}={\frac {dY_{t}}{Y_{t-}}},\quad X_{0}=0.} In layperson's terms, stochastic logarithm of Y {\displaystyle Y} measures the cumulative percentage change in Y {\displaystyle Y} .
Source: Wikipedia "Stochastic logarithm" · CC BY-SA 4.0
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