A new proof for comparison theorems for stochastic differential inequalities with respect to semimartingales

Stochastic Processes and their Applications

Volumn 78, Issue 2, 1998, Pages 155-171

  Ding, Xiaodong ^a   Wu, Rangquan ^a  

^a DONGHUA UNIVERSITY   (China)

Author keywords

60H10; Comparison theorem; Monotone iteration; Semimartingale; Stochastic differential inequality

Indexed keywords

EID: 0038907821     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(98)00051-9     Document Type: Article

References (13)

1. Assing S., Manthey R. The behavior of solutions of stochastic differential inequalities. Probab. Theory Related Fields. 103:1995;493-514.
2. Barlow M., Perkins E. One-dimensional stochastic differential equations involving a singular increasing process. Stochastics. 25:1984;1-20.
3. Bihari I. A generalization of a lemma of Bellman and its application to uniqueness problem of differential equations. Acta Math. Acad. Sci. Hungar. 7:1956;71-94.
4. Ding X., Sun X. A note on monotone iterative technique for one-dimensional stochastic differential equations. Stochastic Anal. Appl. 16(1):1998;65-81.
5. Gei ß C., Manthey R. Comparison theorems for stochastic differential equations in finite and infinite dimensions. Stochastic Process Appl. 53:1994;23-35.
6. Ikeda, N., Watanabe S., 1981. Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam.
7. Jacod, J., Memin, J., 1980. Weak and strong solutions of stochastic differential equations: existence and stability. Stochastic Integrals, Lecture Notes in Math., vol. 851. Springer, Berlin, pp. 169-212.
8. Ladde, G.S., Lakshmikantham, V., Vastasala, A.S., 1985. Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman Monographs and Survey in Pure and Applied Math., vol. 27. Pitman, London.
9. LeGall, J., 1984. One-dimensional stochastic differential equations involving local times of the unknown process. Stochastic Appl. Lecture Notes in Math., vol. 1095. Springer, Berlin, pp. 51-82.
10. Mao, X., 1991. Stability of Stochastic Differential Equations with Respect to Semimartingales. Pitman Research Notes in Math., vol. 251. Pitman, London.
11. Mel'nikov, A.V., 1983. On solutions of stochastic equations with driving semimartingales. Proc. European Young Statisticians Meeting, Leuven, pp. 120-124.
12. Protter, P., 1990. Stochastic Integration and Differential Equations: A New Approach. Springer, Berlin.
13. Situ, R., 1985. On strong solutions and stochastic (pathwise) Bang-Bang control for a non-linear system, 9th World Congress of IFAC, vol. 3, pp. 1433-1438.