# Questions tagged [renewal-processes]

Suppose $\{X_i\}_{i = 1}^\infty$ are i.i.d random variables, such that $P(X_1 > 0) = 1$. Then the corresponding renewal process is $\nu(t) = \max\{n \in \mathbb{N} | \Sigma_{i = 1}^n X_i \leq t\}$. Here $t \in \mathbb{R}_+$.

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### Calculate Expectation of points in a homogenous poission process with parameter $\alpha$ as a renewal process?

If a poisson process $N$ on $[0, \infty )$ has rate $\alpha$ (ie $E N(A)=\alpha m(A)$, $m$ lebesgue measure ) can its points be represented as occurences in a renewal process with interarrival ...
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### renewal equation for $\sim U(0,1)$ interarrivals

renewal equation for $\sim U(0,1)$ interarrivals should be $m(t)=t+\int_0^t{m(t-s)f(s)ds}$ how can this be solved? can I make substitution $y=t-s$ to get $m(t)=t+\int_0^t{m(y)f(y)dy}$ if all I ...
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### Two independent renewal processes

We have two urns (blue and red) that are connected, and two particles, $p_1$ and $p_2$, are traveling between these urns independently. The amount of time $Z_1$ that $p_1$ spends in blue urn is iid ...
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### Waiting time of two independent processes

Suppose that we have two independent alternating renewal processes such that both alternate between states "0" and "1" independently. The amount of time each of them is in state "1" and state "0" ...
166 views

### renewal process question

The question and answer below is related to the renewal process. I'm curious how the "I" changed to "H(T)" as indicated by the yellow boxes. Thanks for spending the time to look over my newbie ...
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### Joint distribution of consecutive renewal times

Consider a discrete analog to the Poisson process. Let the sequence $X_i$ be independent geometrically (with parameter $p$) distributed random variables that signify the inter arrival times of events. ...
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### Renewal process with geometric interarrival times

How would I go about determining the renewal function, $m(n)$, for a general $n$, if the interarrival times, $X_i$ are geometrically distributed with $P(X_i = k) = p \cdot (1-p)^{k-1}$. I believe I ...
Given a renewal process ${X_t}$. How to prove that $\lim_{t\rightarrow \infty}{E[\left(N(t)/t\right)^2]}<\infty$? Does one also have $\lim_{t\rightarrow \infty}{E[\left(N(t)/t\right)^4]}<\infty$ ...