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Elements of Probability Theory

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Semigroups, Boundary Value Problems and Markov Processes

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Abstract

This chapter is intended as a brief introduction to probability theory. Especially, we introduce the general theory of conditional probabilities and conditional expectations which plays a vital role in the study of Markov processes in Chap. 9.

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References

  1. Blumenthal, R.M., Getoor, R.K.: Markov Processes and Potential Theory. Pure and Applied Mathematics, vol. 29. Academic, New York/London (1968)

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  3. Folland, G.B.: Real Analysis: Modern Techniques and Their Applications, 2nd edn. Wiley, New York (1999)

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  4. Lamperti, J.: Stochastic Processes, A Survey of the Mathematical Theory. Applied Mathematical Sciences, vol. 23. Springer, New York/Heidelberg (1977)

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  5. Nishio, M.: Probability Theory (in Japanese). Jikkyo Shuppan, Tokyo (1978)

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Taira, K. (2014). Elements of Probability Theory. In: Semigroups, Boundary Value Problems and Markov Processes. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43696-7_2

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