Branching processes, the Ray-Knight theorem, and sticky brownian motion

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1. [1] M. Amir. Sticky Brownian motion as the strong limit of a sequence of random walks. Stochastic Processes and their Applications, 39:221-237, 1991. Zbl0744.60097MR1136247
2. [2] R.J. Chitashvili. On the nonexistence of a strong solution in the boundary problem for a sticky Brownian motion. Technical Report BS-R8901, Centre for Mathematics and Computer Science, Amsterdam, 1989. Zbl0914.60026
3. [3] W. Feller. On boundaries and lateral conditions for the Kolmogorov equations. Annals of Mathematics, Series 2, 65:527-570, 1957. Zbl0084.35503MR90928
4. [4] J.M. Harrison and A.J. Lemoine. Sticky Brownian motion as the limit of storage processes. Journal of Applied Probability, 18:216-226, 1981. Zbl0453.60072MR598937
5. [5] N. Ikeda and S. Watanabe. Stochastic Differential Equations and Diffusion Processes. North Holand-Kodansha, Amsterdam and Tokyo, 1981. Zbl0495.60005MR637061
6. [6] F.B. Knight. Essentials of Brownian motion and Diffusion, volume 18 of Mathematical Surveys. American Mathematical Society, Providence, Rhode-Island, 1981. Zbl0458.60002MR613983
7. [7] J.F. Le GallCours de troisième cycle, Laboratoire de Probabilités, Paris 6. 1994. 
8. [8] J.W. Pitman and M. Yor. A decomposition of Bessel bridges. Zeitschrift für Wahrscheinlichkeitstheorie, 59:425-457, 1982. Zbl0484.60062MR656509
9. [9] D. Revuz and M. Yor. Continuous martingales and Brownian motion. Springer, Berlin, 1991. Zbl0731.60002MR1083357
10. [10] L.C.G. Rogers and D. Williams. Diffusions, Markov processes and Martingales, vol 2: Itô calculus. Wiley, New York, 1987. Zbl0627.60001MR921238
11. [11] T. Shiga and S. Watanabe. Bessel diffusions as a one-parameter family of diffusion processes. Zeitschrift für Wahrscheinlichkeitstheorie, 27:37-46, 1973. Zbl0327.60047MR368192
12. [12] K. Yamada. Reflecting or sticky Markov processes with Lévy generators as the limit of storage processes. Stochastic Processes and their Applications, 52:135-164, 1994. Zbl0811.60067MR1289173
13. [13] M. Yor. Some remarks concerning sticky Brownian motion. Unpublished, 1989. 
14. [14] M. Yor. Some aspects of Brownian motion, part 1: Some special functionals. Birkhäuser, 1992. Zbl0779.60070MR1193919

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