This is my first post where I'm not requesting help with a problem. Nevertheless, I'm writing here for some book suggestions. After recently finishing my maths degree and as a result of my Random Processes Module, I've developed a keen interest in all things Markov, the lecture notes in this module were poor and feel like I'd like to do some further reading and strengthen ideas that I should have concretely already learnt. It would be great if anyone on here could recommend books oriented around the following; Markov Chains, Queues, Modelling, Invariant Distributions, Brownian Motion etc. Feel free to delve into my previous posts; some give a brief view of what stuff I was learning. Any suggestions would be greatly appreciated :)
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insipidintegrator
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George Cooper
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2Peres Yuval - Brownian motion – Peter Strouvelle Jun 09 '22 at 22:05
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1Some recommendations of stochastic calculus can be found at https://math.stackexchange.com/questions/1188316/good-introductory-book-for-stochastic-calculus-it%C5%8D-calculus. – Integral fan Jun 09 '22 at 23:35
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I would suggest the following books:
- J. M. Steele, Stochastic Calculus and Financial Applications (*)
- R. van Handel, Stochastic Calculus, Filtering, and Stochastic Control (*)
- J. R. Norris, Markov Chains
- Peter Mörters and Yuval Peres, Brownian Motion
- Sheldon Ross, Simulation
- Barry L. Nelson, Stochastic Modeling: Analysis and Simulation
- Oksendal, Stochastic Differential Equations
(*) personal favorites :)
There are also some general books that cover several topics in your list. for example, you can look at Grimmett and Stirzaker: Probability and Random Processes.
Yuval Peres
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Behrad Moniri
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