Linear growth process with immigration rate

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Reference no: EM132516581

Consider a linear growth process with immigration rate k where λn = nλ + k and µn = nµ

i. Write down the di?erence - di?erential equation for this process.

i. Show that M(t) = E{X(t)} for this process satis?es the di?erential equation M0(t) = (λ-µ)M(t) + k i.

Hence show that with initial condition M(0) = i if X(0) = i, Then M(t) = k λ-µ{e(λ-µ)t -1}+ ie(λ-µ)t, λ 6= µ.

Reference no: EM132516581

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