Looking for text on stochastic processes

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Discussion Overview

The discussion revolves around recommendations for introductory texts on stochastic processes, with a focus on specific topics such as Poisson processes, Markov chains, renewal theory, queuing models, and reliability. Participants also explore the necessity of measure theory for understanding stochastic calculus and seek resources to build a foundational background in that area.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant prefers an introductory text covering various topics in stochastic processes, including a desire to learn about stochastic calculus and measure theory.
  • Another participant suggests "Stochastic Processes in Physics and Chemistry" by van Kampen, noting it is more of a collection of methods and problems than a traditional textbook.
  • A participant expresses a preference for mathematics/economics applications over scientific ones and questions whether a background in general chemistry and physics is necessary for understanding the suggested book.
  • Feller's two-volume set on probability is recommended by multiple participants, with emphasis on the second volume's content and potential introduction to measure theory.
  • One participant suggests that a closer-to-mathematics textbook might be more suitable as a main text while still exploring broader applications through other texts.

Areas of Agreement / Disagreement

Participants generally agree on the value of Feller's texts and van Kampen's book, but there is no consensus on the necessity of a scientific background for understanding the mathematical aspects of stochastic processes.

Contextual Notes

Some participants express uncertainty about the required background knowledge in measure theory and its relevance to stochastic calculus, indicating a need for further exploration of foundational texts.

Gridvvk
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An introductory text is preferable. Topics relevant (not a deal-breaker if not covered): Poisson process, Markov chains, renewal theory, models for queuing, and reliability.

Also, in the future I'd like to dabble in stochastic calculus, but my background in measure theory is non-existent. I've heard measure theory is a necessity for stochastic calc., so what are some good sources to build a relevant background in measure theory needed for stochastic calc.?

Thanks for any feedback.

Edit: After posting this I've realized there is a section solely for learning materials. Mod. please move if post is in wrong section.
 
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What field are you more inclined to? Science or mathematics/economy?

For science, the book

van Kampen, Stochastic Processes in Physics and Chemistry, Third Edition (North-Holland Personal Library)

https://www.amazon.com/dp/0444529659/?tag=pfamazon01-20

might be useful to you. More a collection of methods and problems than an introductory textbook, but has some interesting insights scattered throughout the text.
 
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Thanks for the suggestion! The field I'll probably be working with is more-so mathematics/economics (finance) than actual science.

The same methods probably apply in a non-scientific setting. Would general chemistry and standard physics I & II sequence be enough background for the scientific principles in the book? I don't mind the science, but if I have to go out of my way to learn it in order to understand the math, then it might be a distraction.
 
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Gridvvk said:
Thanks for the suggestion! The field I'll probably be working with is more-so mathematics/economics (finance) than actual science.

The same methods probably apply in a non-scientific setting. Would general chemistry and standard physics I & II sequence be enough background for the scientific principles in the book? I don't mind the science, but if I have to go out of my way to learn it in order to understand the math, then it might be a distraction.

Then I think you better try some closer to mathematics textbook as a main text, and peek into van Kampen/others just to get broader view of things and applications.
 
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R136a1 said:
What about Feller's excellent two volume set on probability? https://www.amazon.com/dp/0471257087/?tag=pfamazon01-20
Especially the second volume seems to have some good stuff. There might also be an introduction to measure theory in the book.

Thanks volume 1 is pretty comprehensive and meets my needs. Volume 2 talks about measures.
 
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