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I was wondering if someone could recommend good books on stochastic processes

  • with measure theory treatment
  • with not much or no measure theory treatment

for each, it would be nice to have some books for introductory level, mid-level to comprehensive level respectively. They can be either classical or recently published, either continuous, discrete or both.

Thanks in advance!

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As a mathematician it feels really horrible (to me) to do it in a non-measure theoretic sense, things get much more messy and less rigorous then. – Jonas Teuwen Feb 7 '11 at 23:19
@Jonas T: one can just contribute to those with measure theory treatments. Thanks! – Tim Feb 7 '11 at 23:32
@Jonas Teuwen , is it possible to after basic probability & statistics course, go directly to the measure theory firstly and then to the stochastic processes ? Because I'm bachelor student in applied maths in Sweden, in our program, stochastic processes is not obligatory, another elective option is mathematical modelling 2. I'm not sure whether it's better to learn "measure" based stochastic process on my own directly. – Xingdong Oct 14 '11 at 17:34
@Xingdong: Hi. I think it is possible if you have also done a course in real analysis. Depending on how "mathematically mature" you are it can be quite easy to learn the basics. – Jonas Teuwen Oct 14 '11 at 19:13

Some good books include:

  • Stochastic Processes by Sheldon Ross (no measure theory)
  • Introduction to Probability Models by Sheldon Ross (no measure theory)
  • Stochastic Processes by J.L.Doob (measure theory)
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