Abstract
In this book we have mainly studied (temporally homogeneous) Markov transition functions with only informal references to the random variables which actually form the Markov processes themselves (see Sect. 9.1). In this chapter we study this neglected side of our subject. The discussion will have a more measure-theoretical flavor than hitherto. Section 12.4 is devoted to examples of multi-dimensional diffusion processes. More precisely, we prove that reflecting, absorbing and drifting barrier Brownian motions are typical examples of multi-dimensional diffusion processes.
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References
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Taira, K. (2014). Markov Processes Revisited. 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_12
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DOI: https://doi.org/10.1007/978-3-662-43696-7_12
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