Stochastic logarithm
In stochastic calculus, stochastic logarithm of a semimartingale formula_1such that formula_2 and formula_3 is the semimartingale formula_4 given byformula_5In layperson's terms, stochastic logarithm of formula_1 measures the cumulative percentage change in formula_1. Notation and terminology. The process formula_4 obtained above is commonly denoted formula_9. The terminology "stochastic logarithm" arises from the similarity of formula_9 to the natural logarithm formula_11: If formula_1 is absolutely continuous with respect to time and formula_13, then "formula_4" solves, path-by-path, the differential equation formula_15whose solution is formula_16.