Maximum likelihood drift estimation for multiscale diffusions

Stochastic Processes and their Applications

Volumn 119, Issue 10, 2009, Pages 3173-3210

  Papavasiliou, A ^a   Pavliotis, G A ^b   Stuart, A M ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Averaging; Homogenization; Maximum likelihood; Multiscale diffusions

Indexed keywords

AVERAGING; COARSE-GRAINED; EXPLICIT FORMULA; HOMOGENIZATION; HOMOGENIZATION PROBLEMS; LOG-LIKELIHOOD FUNCTIONS; MAXIMUM LIKELIHOOD ESTIMATOR; MULTISCALE DIFFUSION; MULTISCALE DIFFUSIONS; SMALL SCALE; STOCHASTIC DIFFERENTIAL EQUATIONS;

ASYMPTOTIC ANALYSIS; DIFFERENTIAL EQUATIONS; DIFFUSION; MOLECULAR DYNAMICS; PARAMETER ESTIMATION;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 69849095791     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2009.05.003     Document Type: Article

References (41)

1. Ait-Sahalia Y., Mykland P.A., and Zhang L. How often to sample a continuous-time process in the presence of market microstructure noise. Rev. Financ. Studies 18 (2005) 351-416
2. Ait-Sahalia Y., Mykland P.A., and Zhang L. A tale of two time scales: Determining integrated volatility with noisy high-frequency data. J. Amer. Statist. Assoc. 100 (2005) 1394-1411
3. Bakry D., Cattiaux P., and Guillin A. Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré. J. Funct. Anal. 254 3 (2008) 727-759
4. Battacharya R. A central limit theorem for diffusions with periodic coefficients. Ann. Probab. 13 (1985) 385-396
5. Battacharya R. Multiscale diffusion processes with periodic coefficients and an application to solute transport in porous media. Ann. Appl. Probab. 9 4 (1999) 951-1020
6. Bensoussan A., Lions J.-L., and Papanicolaou G. Asymptotic Analysis for Periodic Structures. Studies in Mathematics and its Applications vol. 5 (1978), North-Holland Publishing Co., Amsterdam
7. Bhattacharya R.N., Gupta V.K., and Walker H.F. Asymptotics of solute dispersion in periodic porous media. SIAM J. Appl. Math 49 1 (1989) 86-98
8. Bhattacharya R.N., and Waymire E.C. Stochastic Processes with Applications (1990), Wiley, New York
9. Cioranescu D., and Donato P. An Introduction to Homogenization (1999), Oxford University Press, New York
10. Dudley R.M. A course on empirical processes. École d'été de probabilités de Saint-Flour, XII-1982. Lecture Notes in Math. vol. 1097 (1984), Springer, Berlin 1-142
11. E W., Liu D., and Vanden-Eijnden E. Analysis of multiscale methods for stochastic differential equations. Comm. Pure Appl. Math. 58 11 (2005) 1544-1585
12. Elworthy K.D. Stochastic Differential Equations on Manifolds. London Mathematical Society Lecture Note Series vol. 70 (1982), Cambridge University Press, Cambridge-New York
13. Ethier S.N., and Kurtz T.G. Markov Processes. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics (1986), John Wiley & Sons Inc, New York
14. Evans L.C. Partial Differential Equations (1998), AMS, Providence, Rhode Island
15. Fouque J.-P., Papanicolaou G.C., and Sircar R.K. Derivatives in Financial Markets with Stochastic Volatility (2000), Cambridge University Press, Cambridge
16. Freǐdlin M.I. The Dirichlet problem for an equation with periodic coefficients depending on a small parameter. Teor. Verojatnost. i Primenen. 9 (1964) 133-139
17. Freidlin M.I., and Wentzell A.D. Random Perturbations of Dynamical Systems (1984), Springer-Verlag, New York
18. Givon D., Kevrekidis I.G., and Kupferman R. Strong convergence schemes of projective integration schemes for singularly perturbed stochastic differential equations. Commun. Math. Sci. 4 4 (2006) 707-729
19. Givon D., Kupferman R., and Stuart A.M. Extracting macroscopic dynamics: Model problems and algorithms. Nonlinearity 17 6 (2004) R55-R127
20. Has'minskiǐ R.Z. Stochastic Stability of Differential Equations. Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis vol. 7 (1980), Sijthoff & Noordhoff, Alphen aan den Rijn
21. Kabanov Y., and Pergamenshchikov S. Two-scale Stochastic Systems. Applications of Mathematics vol. 49 (2003), Springer-Verlag, Berlin Asymptotic analysis and control, Stochastic Modelling and Applied Probability
22. Karatzas I., and Shreve S.E. Brownian Motion and Stochastic Calculus. second edition. Graduate Texts in Mathematics vol. 113 (1991), Springer-Verlag, New York
23. Kutoyants Y.A. Statistical Inference for Ergodic Diffusion Processes. Springer Series in Statistics (2004), Springer-Verlag London Ltd., London
24. Nelson E. Dynamical Theories of Brownian motion (1967), Princeton University Press, Princeton, NJ
25. S. Olhede, G.A. Pavliotis, A. Sykulski, Multiscale inference for high frequency data, 2008 (preprint)
26. Olla S. Homogenization of Diffusion Processes in Random Fields. Lecture Notes (1994)
27. Papanicolaou G.C. Some probabilistic problems and methods in singular perturbations. Rocky Mountain J. Math. 6 4 (1976) 653-674
28. Papanicolaou G.C. Introduction to the asymptotic analysis of stochastic equations. Modern Modeling of Continuum Phenomena (Ninth Summer Sem. Appl. Math., Rensselaer Polytech. Inst., Troy, NY, 1975). Lectures in Appl. Math. vol. 16 (1977), Amer. Math. Soc., Providence, RI 109-147
29. Papanicolaou G.C., Stroock D.W., and Varadhan S.R.S. Martingale approach to some limit theorems. Papers from the Duke Turbulence Conference (Duke Univ., Durham, NC, 1976), Paper No. 6. Duke Univ. Math. Ser. vol. III (1977), Duke Univ, Durham, NC pp. ii+120
30. Papanicolaou G.C. Asymptotic analysis of stochastic equations. Studies in Probability Theory. MAA Stud. Math. vol. 18 (1978), Math. Assoc. America, Washington, DC 111-179
31. Pardoux E. Homogenization of linear and semilinear second order parabolic pdes with periodic coefficients: A probabilistic approach. J. Funct. Anal. 167 (1999) 498-520
32. Pardoux E., and Veretennikov A.Yu. On the Poisson equation and diffusion approximation. I. Ann. Probab. 29 3 (2001) 1061-1085
33. Pardoux È., and Veretennikov A.Yu. On Poisson equation and diffusion approximation. II. Ann. Probab. 31 3 (2003) 1166-1192
34. Pardoux E., and Veretennikov A.Yu. On the Poisson equation and diffusion approximation. III. Ann. Probab. 33 3 (2005) 1111-1133
35. Pavliotis G.A., and Stuart A.M. White noise limits for inertial particles in a random field. Multiscale Model. Simul. 1 4 (2003) 527-533 (electronic)
36. Pavliotis G.A., and Stuart A.M. Parameter estimation for multiscale diffusions. J. Stat. Phys. 127 4 (2007) 741-781
37. Pavliotis G.A., and Stuart A.M. Multiscale Methods. Texts in Applied Mathematics vol. 53 (2008), Springer, New York Averaging and homogenization
38. Prakasa Rao B.L.S. Statistical Inference for Diffusion Type Processes. Kendall's Library of Statistics vol. 8 (1999), Edward Arnold, London
39. van Zanten J.H. A note on consistent estimation of multivariate parameters in ergodic diffusion models. Scand. J. Statist. 28 4 (2001) 617-623
40. Vanden-Eijnden E. Numerical techniques for multi-scale dynamical systems with stochastic effects. Commun. Math. Sci. 1 2 (2003) 385-391
41. Villani C. Hypocoercivity (2008), AMS