Let ({N(t), t geq 0}) be a nonhomogeneous Poisson process with intensity function (lambda(t)) and trend function

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Let \(\{N(t), t \geq 0\}\) be a nonhomogeneous Poisson process with intensity function \(\lambda(t)\) and trend function

\[\Lambda(t)=\int_{0}^{t} \lambda(x) d x\]

Check whether the stochastic process \(\{X(t), t \geq 0\}\) with \(X(t)=N(t)-\Lambda(t)\) is a martingale.

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