I cannot find a proper definition of multivariate martingale. If each component is $1$-dimensional martingale is it enough for a $d$-dimensional process to be a martingale?
Thanks.
2026-04-08 17:27:03.1775669223
Definition of multivariate martingale
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You mean the parameter set is still one-dimensional, and the values are in a vector space like $\mathbb R^n$? Then yes, the definition can be that each component is individually a martingale. Or abstractly that when we apply any linear functional, the result is a scalar-valued martingale.
"Multivariate martingale" might also mean a situation where "time" is replaced by a multi-dimensional parameter set.