List questions from renewal-processes

Published on 09 Jan 2021 - 23:20

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What distribution has the sum of two finite independent sequences of i.i.d. exponential random variables?

Published on 18 Jan 2021 - 19:51

338

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Prove that each renewal process with linear renewal function is Poisson

Published on 19 Jan 2021 - 15:30

64

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Two-dimensional renewal equations — a confusing condition

Published on 01 Feb 2021 - 12:34

49

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Prove the given identity if the probability density function of the length of the intervals of a renewal random process is given.

Published on 09 Feb 2021 - 22:19

103

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Question on Renewal Processes

Published on 26 Feb 2021 - 6:28

109

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Key Renewal and Renewal Type Equations: Finding $E[X_{N(t)+1}^k]$

Published on 28 Feb 2021 - 23:43

555

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Deriving the Key Renewal Theorem from Blackwell's Theorem.

Published on 05 Mar 2021 - 8:02

34

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"First principles" proof of the limit of the expected excess of the uniform renewal function

Published on 18 Apr 2021 - 10:09

33

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Best estimate of the failure rate of a point process

Published on 06 Jul 2021 - 0:35

199

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Ladder variables, Durrett Exercise 5.4.2

Published on 14 Jul 2021 - 3:12

430

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Laplace transform of the Weibull distribution for $\kappa>1$

Published on 01 Aug 2021 - 17:45

118

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I used to think a Poisson process is the only point process with constant event rate.

Published on 29 Sep 2021 - 4:55

214

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Wrong expected value definition in book?

Published on 20 Nov 2021 - 13:09

38

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For a Poisson process, prove $P[\lim_{t\to\infty} (1+ \frac{m(t)}{tN(t)})^{N(t)} = e^{\lambda}] = 1$

Published on 06 Dec 2021 - 22:27

List Question

A probability problem in discrete times.

What distribution has the sum of two finite independent sequences of i.i.d. exponential random variables?

Prove that each renewal process with linear renewal function is Poisson

Two-dimensional renewal equations — a confusing condition

Prove the given identity if the probability density function of the length of the intervals of a renewal random process is given.

Question on Renewal Processes

Key Renewal and Renewal Type Equations: Finding $E[X_{N(t)+1}^k]$

Deriving the Key Renewal Theorem from Blackwell's Theorem.

"First principles" proof of the limit of the expected excess of the uniform renewal function

Best estimate of the failure rate of a point process

Ladder variables, Durrett Exercise 5.4.2

Laplace transform of the Weibull distribution for $\kappa>1$

I used to think a Poisson process is the only point process with constant event rate.

Wrong expected value definition in book?

For a Poisson process, prove $P[\lim_{t\to\infty} (1+ \frac{m(t)}{tN(t)})^{N(t)} = e^{\lambda}] = 1$

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