Abstract
This chapter contains a treatment of Feller’s seminal contribution to a comprehensive theory of one-dimensional diffusions.
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Notes
- 1.
Especially see Feller (1957) in this regard.
- 2.
See the survey article by Peskir (2015) for a penetrating overview.
- 3.
Throughout, BCPT refers to Bhattacharya and Waymire (2016), A Basic Course in Probability Theory.
- 4.
See BCPT, pp. 6, 228.
- 5.
See BCPT p. 250.
- 6.
Dynkin (1965), Vol 1, Theorem 3.6, p.92.
- 7.
Bhattacharya and Waymire (2021), p. 85–86, Proposition 7.15 and Remark 7.8.
- 8.
Bhattacharya and Waymire (2021), Theorem 19.3, p. 230.
- 9.
See Bhattacharya and Waymire (2021), Corollary 7.12, p. 82.
- 10.
See Itô and McKean (1965), pp.167–176.
- 11.
See Itô and McKean (1963).
- 12.
- 13.
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Bhattacharya, R., Waymire, E. (2023). Construction of One-Dimensional Diffusions by Semigroups. In: Continuous Parameter Markov Processes and Stochastic Differential Equations. Graduate Texts in Mathematics, vol 299. Springer, Cham. https://doi.org/10.1007/978-3-031-33296-8_21
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