The Martingale Property in the Context of Stochastic Differential Equations
Johannes Ruf
TL;DR
This paper investigates the conditions under which a nonnegative local martingale derived from a stochastic differential equation is a true martingale, establishing an integral test criterion for this property.
Contribution
It provides a necessary and sufficient integral test condition for the martingale property of local martingales associated with SDE solutions.
Findings
The martingale property is characterized by an integral test.
The criterion is both necessary and sufficient.
The results clarify the conditions for martingale behavior in SDE contexts.
Abstract
This note studies the martingale property of a nonnegative, continuous local martingale Z, given as a nonanticipative functional of a solution to a stochastic differential equation. The condition states that Z is a (uniformly integrable) martingale if and only if an integral test of a related functional holds.
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