Intrinsic location parameter of a diffusion process

Electronic Journal of Probability

Volumn 7, Issue , 2002, Pages 1-23

  Darling, R W R ^a  

^a NATIONAL SECURITY AGENCY   (United States)

Author keywords

Forwardbackwards SDE; Gamma martingale; Harmonic map; Intrinsic location parameter; Nonlinear heat equation; Stochastic differential equation

Indexed keywords

EID: 1842536995     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v7-102     Document Type: Article

References (38)

1. Sun-ichi Amari. Differential-geometrical methods in statistics. Springer-Verlag, New York, 1985. Lecture Notes in Statistics 28.
2. Marc Arnaudon. Espérances conditionnelles et C-martingales dans les varietes. In Séminaire de Probabilités XXVIII, pages 300-311. Springer, 1994. Lecture notes in mathematics 1583.
3. Marc Arnaudon and Anton Thalmaier. Complete lifts of connections and stochastic Jacobi fields. J. Math. Pures Appl. (9), 77(3):283-315, 1998.
4. Marc Arnaudon and Anton Thalmaier. Stability of stochastic differential equations in manifolds. In Séminaire de Probabilités XXXII, J. Azema, M. Emery, M. Ledoux and M. Yor, (eds.), pages 188-214. Springer, Berlin, 1998. Lecture Notes in Mathematics 1686.
5. Ole E. Barndorff-Nielson. Parametric statistical models and likelihood. Springer-Verlag, New York, 1988. Lecture notes in Statistics 50.
6. Yung Mei Chen and Wei Yue Ding. Blow-up and global existence for heat flows of harmonic maps. Invent. Math, 99(3):567-578, 1990.
7. Dan Crisan and Terry Lyons. Nonlinear filtering and measure-valued processes. Probab. Theory Related Fields, 109(2):217-244, 1997.
8. R. W. R. Darling. Geometrically instrinsic nonlinear recursve filters I: algorithms. Preprint (1997), available as No. 494 at http://www.stat.berkeley.edu/tech-reports.
9. R. W. R. Darling. Geometrically instrinsic nonlinear recursve filters II: foundations. Preprint (1998), available as No. 512 at http://www.stat.berkeley.edu/tech-reports.
10. R. W. R. Darling. Differential Forms and Connections. Cambridge University Press, 1994.
11. R. W. R. Darling. Constructing gamma-martingales with prescribed limit using backwards SDE. Ann. Probab., 23(3):1234-1261, 1995.
12. R. W. R. Darling. Martingales on noncompact manifolds: maximal inequalities and prescribed limits. Ann. Inst. H. Poincare Probab. Statist., 32(4):431-454, 1996.
13. R. W. R. Darling and Etienne Pardoux. Backwards SDE with random terminal time, and applications to semilinear elliptic PDE. Ann. Probab., 25(3):1135-1159, 1997.
14. J. L. Doob. A probability approach to the heat equation. Trans. Amer. Math. Soc., 80:216-280, 1955.
15. J. Eells and L. Lemaire. A report on harmonic maps. Bull. London Math. Soc., 10(1):1-68, 1978.
16. J. Eells and L. Lemaire. Another report on harmonic maps. Bull. London Math. Soc., 20(5):385-524, 1988.
17. James Eells, Jr. and J. H. Sampson. Harmonic mappings of Riemannian manifolds. Amer. J. Math., 86:109-160, 1964.
18. K. D. Elworthy. Stochastic Differential Equations on Manifolds. Cambridge University Press, Cambridge, 1982.
19. Michel Emery. Convergence des martingales dans les varietes. Asterisque, (132):47-63, 1985. Colloquium in honor of Laurent Schwartz, Vol 2. (Palaiseau, 1983).
20. Michel Emery. Stochastic Calculus in Manifolds. Springer-Verlag, Berlin, 1989. With an appendix by P.-A. Meyer.
21. Michel Emery and G. Mokobodzki. Sur le barycentre d’une probabilite dans une variete. In Seminaire de Probabilities XXV, pages 220-233. Springer, Berlin, 1991.
22. Richard S. Hamilton. Harmonic m,a,p.s of manifolds with boundary. Springer-Verlag, Berlin, 1975. Lecture notes in mathematics, Vol. 471.
23. Harrie Hendriks. A Cramer-Rao type lower bound for estimators with values in a manifold. J. Multivariate Analysis, 38(2):245-261, 1991.
24. Wilfrid S. Kendall. Probability, convexity, and harmonic maps with small image I: Uniqueness and fine existence. Proc. London Math. Soc. (3), 61(2):371-406, 1990.
25. Wilfrid S. Kendall. Probability, convexity, and harmonic maps II: Smoothness via probabilistic gradient inequalities. J. Funct. Anal., 126(1):228-257, 1994.
26. O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Ural’ceva. Linear and Quasilinear Equations of Parabolic Type. American Mathematical Society, 1968. Translations of Math. Monographs 23.
27. T. J. Lyons. What you can do with n observations. In Geometrization of statistical theory, T. J. Dodson (ed.), pages 28-31. ULDM Publ., Oct 1987. Proceedings of the GST Workshop, University of Lancaster.
28. P. Del Moral. Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems. Ann. Appl. Probab., 8(2):438-495, 1998.
29. Michael K. Murray and John W. Rice. Differential Geometry and Statistics. Chapman and Hall, London, 1993.
30. J. M. Oller and J. M. Corcuera. Intrinsic analysis of statistical estimation. Ann. Statist., 23(5):1562-1581, 1995.
31. E. Pardoux and S. Peng. Backward stochastic differential equations and quasilinear parabolic partial differential equations. In Stochastic Partial Differential Equations and Their Applications, B. L. Rozowskii and R. B. Sowers (eds.), pages 200-217. Springer-Verlag, Berlin, 1992. Lecture notes in control and information sciences 176.
32. Jean Picard. Martingales on Riemannian manifolds with prescribed limit. J. Funct. Anal., 99(2):223-261, 1991.
33. Jean Picard. Barycentres et martingales sur une variete. Ann. Inst. H. Poincare Probab. Statist., 30(4):647-702, 1994.
34. Daniel Revuz and Marc Yor. Continuous Martingales and Brownian Motion. Springer-Verlag, Berlin, 1991.
35. Robert S. Strichartz. Sub-Riemannian geometry. J. Differential Geom, 24(2):221-263, 1986. Corrections 30(1989), 595-596.
36. Michael Struwe. Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems. Springer-Verlag, Berlin, 1996.
37. Anton Thalmaier. Brownian motion and the formation of singularities in the heat flow for harmonic maps. Probab. Theory Related Fields, 105(3):335-367, 1996.
38. Anton Thalmaier. Martingales on Riemannian manifolds and the nonlinear heat equation. In Stochastic Analysis and applications, I. M. Davies, A. Truman and K. D. Elworthy, (eds.), pages 429-440. World Sci. Publishing, River Edge, NJ, 1996.