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A stochastic process describes the evolution of random variables/systems over time and/or space and/or any other index set. It has applications in areas such as econometrics, weather, signal processing, etc. Examples: Gaussian process, Markov process, etc.

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1 answer
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Is this problem worked out correctly? [closed]

Calls are received at a company call center according to a Poisson process at the rate of five calls per minute. (a) Find the probability that no call occurs over a 30-second period. (b) Find t …
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1 vote
1 answer
76 views

Compute the Limiting Distribution

Consider the transition matrix $ P = \begin{bmatrix} 1-p&p\\ q&1-q \end{bmatrix} $ for general $2$-state Markov Chain $(0 \le p, q\le 1)$. Find the limiting distribution (if …
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1 vote
1 answer
266 views

Expectation of arrival times

Let $(N_t)_t$ be a Poisson process with parameter λ = 2. By $τ_k$ denote the time of the k-th arrival (k = 1, 2, . . .), and by $ρ_k = τ_k −τ_{k−1}$ - the interarrival time between the (k−1)th and …
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1 vote
1 answer
3k views

What is the difference between time, arrival-time, and inter-arrival-time is poisson process?

Let $(N_t)_t$ be a Poisson process with parameter λ = 2. By $τ_k$ denote the time of the k-th arrival (k = 1, 2, . . .), and by $ρ_k = τ_k −τ_{k−1}$ - the interarrival time between the (k−1)th and …
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3 votes
1 answer
679 views

What is the difference between a Random Vector (Joint r.v.) and a Random Process?

What is the difference between a Random Vector (Joint r.v.) and a Random Process? Kindly, explain with a simple example (like toss of a coin, roll of a die, picking a card, etc.). Note. As far as I un …
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0 votes
1 answer
164 views

What type of statistics is Probability? [closed]

Are probability, random-variable, and stochastic process part of descriptive statistics or inferential statistics?
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249 views

Some simple examples to understand various types of Stochastic Processes

I am trying to understand various types of stochastic processes through some analogical examples using simple experiments like a coin toss or die roll. The book of Hwei Hsu (Chapter-5, Page-162-165, …
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2 votes
1 answer
793 views

How can I compute expected return time of a state in a Markov Chain?

I was watching a YouTube video regarding the calculation of expected return time of a Markov Chain. https://www.youtube.com/watch?v=X_Ll0-Ytu7U&vl=en I haven't understood the calculation of $m_{12}$ …
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3 votes
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Manually simulating Poisson Process in R

The following problem tells us to generate a Poisson process step by step from $\rho$ (inter-arrival time), and $\tau$ (arrival time). One of the theoretical results presented in the lectures g …
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