One-dimensional stochastic differential equations with singular and degenerate coefficients

Sankhya: The Indian Journal of Statistics

Volumn 67, Issue 1, 2005, Pages 19-45

  Bass, Richard F ^a   Chen, Zhen Qing ^b  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Comparison principle; Degenerate coefficients; Pathwise uniqueness; Singular drift; Stochastic differential equations; Strong solution

Indexed keywords

EID: 31344445888     PISSN: 09727671     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. BARLOW, M. (1982). One dimensional stochastic differential equations with no strong solutions. J. London Math. Soc. 26, 335-347.
2. BARLOW, M.T. and PERKINS, E. (1984). One-dimensional stochastic differential equations involving a singular increasing process. Stochastics 12, 229-249.
3. BASS, R. (1997). Diffusions and Elliptic Operators. Springer, New York.
4. BASS, R. and CHEN, Z.-Q. (2001). Stochastic differential equations for Dirichlet processes. Probab. Theory Relat. Fields, 121, 422-446.
5. BURDZY, K., CHEN, Z.-Q. and SYLVESTER, J. (2004). Heat equation and reflected Brownian motion in time dependent domains. Ann. Probab. 32, 775-804.
6. ENGELBERT, H.J. and SCHMIDT, W. (1985). On solutions of one-dimensional stochastic differential equations without drift. Z. Wahrsch. 68, 287-314.
7. HARRISON, J.M. and SHEPP, L.A. (1981). On skew Brownian motion. Ann. Probab. 9, 309-313.
8. JACOD, J. and SHIRYAEV, A.N. (1987). Limit Theorems for Stochastic Processes. Springer-Verlag, Heidelberg.
9. KANEKO, H. and NAKAO, S. (1988). A note on approximation for stochastic differential equations. Séminaire de Probabilités XXII, 155-162, Springer, Berlin.
10. KARATZAS, I. and SHREVE, S.E. (1994). Brownian Motion and Stochastic Calculus, Second Edition. Springer-Verlag, New York.
11. LE GALL, J.F. (1983). Applications du temps local aux équations différentielles stochastiques unidimensionnelles. Séminaire de Probabilités XVII, Lecture Notes on Mathematics 986, J. Azma and M. Yor, eds., Springer, Berlin-New York, 15-31.
12. LE GALL, J.F. (1984). One-dimensional stochastic differential equations involving the local times of the unknown process. In Stochastic Analysis and Applications (Proceedings, Swansea 1983), Lecture Notes on Mathematics 1095, A. Truman and D. Williams, eds., Springer, Berlin, 51-82.
13. NAKAO, S. (1972). On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations. Osaka J. Math. 9, 513-518.
14. REVUZ, D. and YOR, M. (1991). Continuous Martingales and Brownian Motion. Springer-Verlag, Berlin.
15. YAMADA, T. and WATANABE, S. (1971). On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11, 155-167.
16. ZHANG, T.S. (1994). On the strong solutions of one-dimensional stochastic differential equations with reflecting boundary. Stochastic Process. Appl. 50, 135-147.