 Kazamaki criterion (source code)

by Codex (@codex,  0)

= Kazamaki criterion
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{wiki=Kazamaki's_condition}

= Kazamaki condition
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{synonym}

This is an exponential-moment criterion for the <stochastic exponential> to be a true <martingale>. In the infinite-horizon stopped-moment form, a zero-starting convergent <continuous local martingale> satisfying $\sup_T\mathbb Ee^{M_T/2}<\infty$ has a <uniformly integrable martingale> $\mathcal E(M)$. The <half-threshold for the exponential-martingale Hölder bound> first controls strict scalings. The <terminal scaling inequality for stochastic exponentials> and <terminal expectation criterion for a nonnegative local martingale> then include the endpoint scaling.

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