On Émery's inequality and a variation-of-constants formula

Stochastic Analysis and Applications

Volumn 25, Issue 2, 2007, Pages 353-379

  Reiß, Markus ^a   Riedle, Markus ^b   Van Gaans, Onno ^c  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b HUMBOLDT UNIVERSITY   (Germany)

^c LEIDEN UNIVERSITY   (Netherlands)

Author keywords

mery's inequality; Functional Lipschitz coefficient; Linear drift; Semimartingale; Stochastic delay differential equation; Variation of constants formula

Indexed keywords

EID: 33947163352     PISSN: 07362994     EISSN: 15329356     Source Type: Journal    
DOI: 10.1080/07362990601139586     Document Type: Article

References (12)

1. Da Prato, G., and Zabczyk, J. 1992. Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and Its Applications, Vol. 45, Cambridge University Press, Cambridge.
2. Dellacherie, C., and Meyer, P.-A. 1975. Probabilité et Potentiel. Chapitres I à IV, Édition entièrement refondue, Hermann, Paris.
3. Dellacherie, C., and Meyer, P.-A. 1980. Probabilité et potentiel. Chapitres V à VIII, Théorie des martingales, Édition entièrement refondue, Hermann, Paris.
4. Dunford, N., and Schwartz, J.T. 1957. Linear Operators. Part 1: General Theory, Wiley Interscience, New York.
5. Émery, M. 1978. Stabilité des solutions des équations différentielles stochastiques applications aux intégrales multiplicatives stochastiques. Z. Wahrscheinlichkeitstheorie verw. Gebiete 41:241-262.
6. Hale, J.K., and Verduyn Lunel, S.M. 1993. Introduction to Functional Differential Equations. Applied Mathematical Sciences 99. Springer-Verlag, New York.
7. Jacod, J., and Shiryaev, A.N. 2003. Limit Theorems for Stochastic Processes. 2nd ed. Springer-Verlag, Berlin, Heidelberg.
8. Kallenberg, O. 2002. Foundations of Modern Probability. 2nd ed. Springer-Verlag, New York.
9. Karatzas, I., and Shreve, S.E. 1991. Brownian Motion and Stochastic Calculus. 2nd ed. Graduate Texts in Mathematics 113. Springer-Verlag, New York.
10. Protter, Ph. 1985. Volterra equations driven by semimartingales. Ann. Probab. 13(2):519-530.
11. Protter, Ph. 1990. Stochastic Integration and Differential Equations. A New Approach. Springer-Verlag, Berlin, Heidelberg.
12. Reiß, M., Riedle, M., and van Gaans, O. 2006. Delay differential equations driven by Lévy processes: Stationarity and Feller properties. Stochastic Process. Appl. 116(10):1409-1432.