Laplace approximation of transition densities posed as Brownian expectations

Stochastic Processes and their Applications

Volumn 119, Issue 1, 2009, Pages 208-231

  Markussen, Bo ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Discrete partial observation; Laplace approximation; Maximum a posteriori estimation; Maximum likelihood estimation; Path integral; Renormalized Brownian density; Stochastic differential equation; White noise

Indexed keywords

BLOCK CODES; BROWNIAN MOVEMENT; DIFFERENTIAL EQUATIONS; EQUATIONS OF MOTION; LAPLACE EQUATION; LAPLACE TRANSFORMS; MAXIMUM LIKELIHOOD; MEASUREMENT THEORY; ORDINARY DIFFERENTIAL EQUATIONS; PIECEWISE LINEAR TECHNIQUES; POLYNOMIAL APPROXIMATION; STOCHASTIC CONTROL SYSTEMS; TURBO CODES;

DISCRETE PARTIAL OBSERVATION; LAPLACE APPROXIMATION; MAXIMUM A POSTERIORI ESTIMATION; PATH INTEGRAL; RENORMALIZED BROWNIAN DENSITY; STOCHASTIC DIFFERENTIAL EQUATION;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 57149096941     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2008.01.011     Document Type: Article

References (23)

1. Aït-Sahalia Y. Maximum likelihood estimation of discretely sampled diffusions: A closed form approximation approach. Econometrica 70 (2002) 223-262
2. Y. Aït-Sahalia, Closed-form likelihood expansions for multivariate diffusions, Working Paper, Princeton, 2004. Available from: http://www.princeton.edu/~yacine/research.htm
3. Baudoin F. Conditioned stochastic differential equations: Theory, examples and application to finance. Stochastic Process. Appl. 100 (2002) 109-145
4. Berger J.O. Statistical Decision Theory and Bayes Statistics (1999), Springer Verlag
5. Beskos A., Papaspiliopoulos O., Roberts G.O., and Fearnhead P. Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes. J. R. Statist. Soc. B 68 3 (2006) 333-382
6. Bibby B.M., Jacobsen M., and Sørensen M. Estimating functions for discretely sampled diffusion-type models. In: Ait-Sahalia Y., and Hansen L.P. (Eds). Handbook of Financial Econometrics (2004), North-Holland
7. Clarke F.H. Tonelli's regularity theory in the calculus of variations: Recent progress. Lecture Notes in Math. 1190 (1986) 163-179
8. Bibby B.M., and Sørensen M. Martingale estimation functions for discretely observed diffusion processes. Bernoulli 1 (1995) 17-39
9. de Falco D., and Khandekar D.C. Application of white noise calculus to the computation of Feynman integrals. Stochastic Process. Appl. 29 (1988) 257-266
10. Gill R.D., and Johansen S. A survey of product-integration with a view toward application in survival analysis. Ann. Statist. 18 (1990) 1501-1555
11. Heston S.L. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6 (1993) 327-343
12. Hida T., Kuo H.-H., Potthoff J., and Streit L. White Noise (1993), Kluwer
13. Kunita H. Stochastic Flows and Stochastic Differential Equations (1990), Cambridge University Press
14. B. Markussen, A statistical approach to large deformation diffeomorphisms, in: Workshop on Generative Model Based Vision at the IEEE Conference on Computer Vision and Pattern Recognition, Washington DC, 2004
15. Markussen B. Large deformation diffeomorphisms with application to optic flow. Computer Vision Image Understanding 106 (2007) 97-105
16. B. Markussen, Inversion of some integral operators with a lattice structure, Working Paper, Department of Natural Sciences, University of Copenhagen, 2008. Available from: http://www.matfys.kvl.dk/~torbenm/publ.dept/2008.html
17. Nualart D. Malliavin Calculus and Related Topics (1995), Springer Verlag
18. Pedersen G.K. Analysis Now (1989), Springer Verlag
19. R. Poulsen, Approximate maximum likelihood estimation of discretely observed diffusion processes, Working Paper No. 29, Center of Analytic Finance, Aarhus, 1999
20. Sørensen H. Parametric inference for diffusion processes observed at discrete points in time: A survey. Int. Statist. Rev. 72 (2004) 337-354
21. Streit L., and Hida T. Generalized Brownian functionals and the Feynman integral. Stochastic Process. Appl. 16 (1984) 55-69
22. Tonelli L. Sur une méthode directe du calcul des variations. Rend. Circ. 39 (1915) 233-264
23. Twining C., and Marsland S. Constructing diffeomorphic representations of non-rigid registrations of medical images. LNCS 2732 (2003) 413-425