Stochastic processes

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Consider a linear growth process with immigration rate k where λn = nλ k and µn = nµi. Write down the difference – differential equation for this process.i. Show that M(t) = E{X(t)} for this process satisfies the differential 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= µ16/05/20200.01appliedsciences