Invariant manifolds for weak solutions to stochastic equations

Probability Theory and Related Fields

Volumn 118, Issue 3, 2000, Pages 323-341

  Filipović, Damir ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034358760     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00008744     Document Type: Article

References (17)

1. Abraham, R., Marsden, J.E., Ratiu, T.: Manifolds, tensor analysis, and applications, Springer-Verlag, Berlin-Heidelberg-New York, 1988
2. Bardi, M., Goatin, P.: Invariant sets for controlled degenerate diffusions: a viscosity solutions approach, Stochastic analysis, control, optimization and applications, Birkhäuser Boston, Boston, MA, pp. 191-208 (1999)
3. Björk, T., Christensen, B.J.: Interest rate dynamics and consistent forward rate curves, Math. Finance 9, 323-348 (1999)
4. Björk, T., Svensson, L.: On the existence of finite dimensional realizations for nonlinear forward rate models, Working paper, Stockholm School of Economics, submitted, 1997
5. Boothby, W.M.: An introduction to differentiable manifolds and Riemannian geometry, second ed., Academic Press, 1986
6. Da Prato, G., Zabczyk, J.: Stochastic equations in infinite dimensions, Cambridge University Press, 1992
7. Emery, M.: Stochastic calculus in manifolds, Springer-Verlag, Berlin-Heidelberg-New York, 1989
8. Filipović, D.: Exponential-polynomial families and the term structure of interest rates, to appear in Bernoulli
9. Filipović, D.: A note on the Nelson-Siegel family, Math. Finance 9, 349-359 (1999)
10. Filipović, D.: Consistency problems for HJM interest rate models, Ph.D. thesis, ETH Zürich, 2000
11. Jachimiak, W.: Stochastic invariance in infinite dimension, Working paper, Polish Academy of Sciences, 1998
12. Milian, A.: Invariance for stochastic equations with regular coefficients, Stochastic Anal. Appl. 15 (1), 91-101 (1997)
13. Revuz, D., Yor, M.: Continuous martingales and Brownian motion, second ed., Grundlehren der mathematischen Wissenschaften, vol. 293, Springer-Verlag, Berlin-Heidelberg-New York, 1994
14. Rudin, W.: Functional analysis, second ed., McGraw-Hill, 1991
15. Stoer, J., Bulirsch, R.: Einführung in die Numerische Mathematik, second ed., vol. II, Springer-Verlag, Berlin-Heidelberg-New York, 1978
16. Tessitore, G., Zabczyk, J.: Comments on transition semigroups and stochastic invariance, Preprint, 1998
17. Zabczyk, J.: Stochastic invariance and consistency of financial models, Preprint, Polish Academy of Sciences, Warsaw, 1999