Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursions

Probability Theory and Related Fields

Volumn 127, Issue 1, 2003, Pages 37-61

  Dawson, Donald A ^a   Li, Zenghu ^b  

^a CARLETON UNIVERSITY   (Canada)

^b BEIJING NORMAL UNIVERSITY   (China)

Author keywords

Dependent spatial motion; Excursion; Immigration; Poisson random measure; Stochastic equation; Superprocess

Indexed keywords

EID: 0141680349     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-003-0278-y     Document Type: Article

References (16)

1. Dawson, D.A.: Measure-Valued Markov Processes. Lect. Notes. Math. 1541, Berlin: Springer-Verlag, 1993, pp. 1-260
2. Dawson, D.A., Vaillancourt, J., Wang, H.: Stochastic partial differential equations for a class of measure-valued branching diffusions in a random medium. Ann. Inst. Henri Poincare, Probabilités and Statistiques 36, 167-180 (2000)
3. Dawson, D.A., Li, Z.H., Wang, H.: Superprocesses with dependent spatial motion and general branching densities. Elect. J. Probab. (25) 6, 1-33 (2001)
4. Ethier, S.N., Kurtz, T.G.: Markov Processes: Characterization and Convergence. New York: Wiley, 1986
5. Fu, Z.F., Li, Z.H.: Measure-valued diffusions and stochastic equations with Poisson process. Osaka J. Math., 2003, submitted, ps and pdf files: math.bnu.edu.cn/~lizh
6. Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. North-Holland/Kodansha, Amsterdam/Tokyo, 1989
7. Konno, N., Shiga, T.: Stochastic partial differential equations for some measure-valued diffusions. Probab. Theory Related Fields 79, 201-225 (1988)
8. Li, Z.H.: Skew convolution semigroups and related immigration processes. Theory Probab. Appl. 46, 274-296 (2002)
9. Li, Z.H., Shiga, T.: Measure-valued branching diffusions: immigrations, excursions and limit theorems. J. Math. Kyoto Univ. 35, 233-274 (1995)
10. Pitman, J., Yor, M.: A decomposition of Bessel bridges. Z. Wahrsch. verw. Geb. 59, 425-457 (1982)
11. Reimers, M.: One dimensional stochastic differential equations and the branching measure diffusion. Probab. Theory Related Fields 81, 319-340 (1989)
12. Shiga, T. : A stochastic equation based on a Poisson system for a class of measure-valued diffusion processes. J. Math. Kyoto Univ. 30, 245-279 (1990)
13. Shiga, T., Watanabe, S.: Bessel diffusions as a one-parameter family of diffusion processes. Z. Wahrsch. verw. Geb. 27, 37-46 (1973)
14. Walsh, J.B.: An Introduction to Stochastic Partial Differential Equations. In: Lect. Notes Math. 1180, Springer-Verlag, 1986, pp. 265-439
15. Wang, H.: State classification for a class of measure-valued branching diffusions in a Brownian medium. Probab. Theory Related Fields 109, 39-55 (1997)
16. Wang, H.: A class of measure-valued branching diffusions in a random medium. Stochastic Anal. Appl. 16, 753-786 (1998)