What is the definition of a nonegative submartingale?
Im not able to find a definition for it anywhere. all the sites about it just assume you know what it is and go on to explain Doob inequalities.
2026-03-28 20:52:25.1774731145
What is a nonegative submartingale?
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$(X_n)$ is a non-negative submartingale if $X_n \geq 0$ almost surely for every $n$ and
$E(X_{n+1}|\mathcal F_n) \geq X_n$ almost surely for each $n$ where $\mathcal F_n$ is the sigma field generated by $X_1,X_2,...,X_n$. (You can also talk about non-negative submartingale relative to a given filtration w.r.t which $(X_n)$ is adapted).