Brownian-time processes: The pde connection and the half-derivative generator

Annals of Probability

Volumn 29, Issue 4, 2001, Pages 1780-1795

  Allouba, Hassan ^a   Zheng, Weian ^b,c  

^a INDIANA UNIVERSITY   (United States)

^b EAST CHINA NORMAL UNIVERSITY   (China)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Brownian time processes; Excursion based brownian time processes; Half derivative generator; Iterated brownian motion; Markov snake

Indexed keywords

EID: 0035470879     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1015345772     Document Type: Article

References (17)

1. ALLOUBA, H. (1999). Measure-valued Brownian-time processes: the PDE connection. Unpublished manuscript.
2. BURDZY, K. (1993). Some path properties of iterated Brownian motion. In Seminar on Stochastic Processes (E. Çinlar, K. L. Chung and M. J. Sharpe, eds.) 67-87. Birkhäuser, Boston.
3. BURDZY, K. (1994). Variation of iterated Brownian motion. In Workshop and Conference on Measure-Valued Processes, Stochastic PDEs and Interacting Particle Systems 35-53. Amer. Math. Soc., Providence, RI.
4. BURDZY, K. and KHOSHNEVISAN, D. (1995). The level sets of iterated Brownian motion. Séminaire de Probabilités XXIX. Lecture Notes in Math. 1613 231-236. Springer, Berlin.
5. BURDZY, K. and KHOSHNEVISAN, D. (1998). Brownian motion in a Brownian crack. Ann. Appl. Probab. 8 708-748.
6. DURRETT, R. (1996). Stochastic Calculus. A Practical Introduction. Probability and Stochastics Series. CRC Press, Boca Raton, FL.
7. ELWORTHY, K. D. (1982). Stochastic Differential Equations on Manifolds. Cambridge Univ. Press.
8. FUNAKI, T. (1979). Probabilistic construction of the solution of some higher order parabolic differential equation. Proc. Japan Acad. Ser. A Math. Sci. 55 176-179.
9. GETOOR, R. (1961). First passage times for symmetric stable processes in space. Trans. Amer. Math. Soc. 101 75-90.
10. HOCHBERG, K. (1996). Composition of stochastic processes governed by higher-order parabolic and hyperbolic equations. J. Theoret. Probab. 9 511-532.
11. KINATEDER, K, MCDONALD, P. and MILLER, D. (1998). Exit time moments, boundary value problems, and the geometry of domains in Euclidean space. Probab. Theory Related Fields 111 469-487.
12. KUNITA, H. (1990). Stochastic Flows and Stochastic Differential Equations. Cambridge Univ. Press.
13. 2 dans le disque unité. C. R. Acad. Sci. Paris Sér. I 317 873-878.
14. LE GALL, J.-F. (1994). A path-valued Markov process and its connections with partial differential equations. In First European Congress of Mathematics 2 185-212. Birkhäuser, Boston.
15. 2 in a domain. Probab. Theory Related Fields 102 393-432.
16. LYONS, T. and ZHENG, W. (1990). On conditional diffusion processes. Proc. Roy. Soc. Edinburgh 115 243-255.
17. ZHENG, W. (1995). Conditional propagation of chaos and a class of quasilinear PDE's. Ann. Probab. 23 1389-1413.