Looking for text on stochastic processes

[Gridvvk]

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.

 

[Jano L.]

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.

 

[Gridvvk]

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.

 

[R136a1]

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.

 

[Jano L.]

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.

 

[Gridvvk]

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.