I consider a semimartingale $(X_t)_{0 \leq t}$.I need that $$ t \mapsto E[X_t] $$ is continous. What kind of properties on $(X_t)$ will ensure that? I mean, if, say, $(X_t)$ has independent increments we know $$ E[X_t] = E[X_0] + t E[X_t-X_0] $$ and the statement is true, but I'm clueless as to approach this issue generally.
2026-04-24 21:26:45.1777066005
When is the mean value function of a semimartingale continuous
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