Stopped Doob inequality for p-TH moment, 0 < p < ∞, stochastic convolution integrals

Stochastic Analysis and Applications

Volumn 19, Issue 5, 2001, Pages 771-798

  Hamedani, Hamideh D ^a   Zangeneh, Bijan Z ^a  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Contraction type evolution operator and martingale; Stochastic convolution integral; Stopped Doob inequality

Indexed keywords

EID: 0035639301     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1081/SAP-120000221     Document Type: Article

References (19)

1. Ahmed, N.U., H. Harbi. Suspension bridge: Stochastic Models and Their Mathematical Analysis. To appear in SIAM Journal of Applied Mathematics.
2. Burkholder, D.L.; Davis, B.J.; Gundy, R.F. Integral inequalities for convex functions of operators on martingales. Proc. 6th Berkeley Symp. Math. Statist. Proba. 1972, 2, 223-240.
3. Da Prato, G.; Zabczyk, J.; Stochastic Equations in Infinite Dimensions, Encyclopedia of Mathematics and its Applications, Rota, G.C., Ed.; Cambridge University Press: Cambridge, 1992; Vol. 45.
4. Hamedani, H.D. Existence and Uniqueness of Solutions for Semilinear Stochastic Equations with Semimonotone Nonlinearities and Martingale Integrators, Preprint, 1999.
5. Ichikawa, A. Semilinear stochastic evolution equations: Boundedness, stability and invariant measures. Stochastics 1984, 12, 1-39.
6. Ichikawa, A. Some inequalities for martingales and stochastic convolutions. Stoch. Anal. Appl. 1986, 4 (3), 329-339.
7. Jacod, J. Calcul Stochastique et Problémes de Martingales; Lecture Notes in Mathematics 714, Springer-Verlag: Berlin, 1979.
8. Karatzas, I.; Shreve, S. Brownian Motion and Stochastic Calculus; Springer: Berlin, 1988.
9. Kotelenez, P. A submartingale type inequality with applications to stochastic evolution equations. Stochastics 1982, 8, 139-151.
10. Kotelenez, P. A stopped Doob inequality for stochastic convolution integrals and stochastic evolution equations. Stoch. Anal. Appl. 1984, 2, 245-265.
11. Métivier, M. Semimartingales; Walter de Gruyter: Berlin, 1982.
12. Métivier, M.; Pellaumail, J. On a stopped Doob's inequality and general stochastic equations. Ann. Prob. 1980, 8 (No. 1), 96-114.
13. Métivier, M.; Pellaumail, J. Stochastic Integration; Academic Press: New York, 1980.
14. Pardoux, E. Intégrales Stochastiques Hilbertiennes, Cahiers de Mathématiques de la Décision, Université Paris-Dauphine, 1976.
15. Rümelin, W. Numerical treatment of stochastic differential equations. SIAM J. Numer. Anal. 1982. 19 (3).
16. Spanos, P.D.; Brebbia, C.A. Computational Stochastic Mechanics; Computational Mechanics Publications: Southampton, 1991.
17. Williams, D. Diffusions-Markov Processes and Martingales; Wiley: New York, 1987; Vol. 2.
18. Zangeneh, B.Z. Semilinear Stochastic Evolution Equations, Ph.D. Thesis, UBC Canada, 1990.
19. Zangeneh, B.Z. Semilinear stochastic evolution equations with monotone nonlinearities. Stochastics and Stochastics Reports 1995, 53 (Numbers 1+2), 129-174.