Verify that the second moment of (N(t)), denoted as (H_{2}(t)=Eleft(N^{2}(t) ight)), satisfies the integral equation [H_{2}(t)=2 H(t)-F(t)+int_{0}^{t}

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Verify that the second moment of $N(t)$, denoted as $H_{2}(t)=E\left(N^{2}(t)\right)$, satisfies the integral equation

\[H_{2}(t)=2 H(t)-F(t)+\int_{0}^{t} H_{2}(t-x) f(x) d x .\]

Verify the equation directly or by applying the Laplace transformation.

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Applied Probability And Stochastic Processes

ISBN: 9780367658496

2nd Edition

Authors: Frank Beichelt

Question Posted: Apr 26, 2024 04:01 PM

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Verify that the second moment of (N(t)), denoted as (H_{2}(t)=Eleft(N^{2}(t) ight)), satisfies the integral equation [H_{2}(t)=2 H(t)-F(t)+int_{0}^{t}

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Applied Probability And Stochastic Processes

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