Let (X(t)=S^{3}(t)-3 t S(t)). Prove that ({X(t), t geq 0}) is a continuous-time martingale, i.e., show that

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Let \(X(t)=S^{3}(t)-3 t S(t)\). Prove that \(\{X(t), t \geq 0\}\) is a continuous-time martingale, i.e., show that

\[E(X(t) \mid X(y), y \leq s)=X(s), \quad s

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