论文信息 - An Ornstein-Uhlenbeck-Type Process Which Satisfies Sufficient Conditions for a Simulation-Based Filtering Procedure

An Ornstein-Uhlenbeck-Type Process Which Satisfies Sufficient Conditions for a Simulation-Based Filtering Procedure

In this article, we verify all the conditions stated in [8] in order for a filtering/estimation procedure based on Monte Carlo simulations of unknown densities of diffusion processes to converge to its theoretical values. In order to verify these hypotheses one needs to use extensively various properties of the diffusion processes and its Euler–Maruyama approximation. In particular, we need to study flow properties, upper and lower bounds for densities and existence of invariant measures and α-mixing properties.

Kazuhiro Yasuda | Arturo Kohatsu-Higa | A. Kohatsu-Higa | Kazuhiro Yasuda

[1] David Nualart Rodón,et al. The Malliavin Calculus and Related Topics , 2006 .

[2] V. Bally. Lower bounds for the density of locally elliptic Itô processes , 2006, math/0702879.

[3] N. Vayatis,et al. Strong Consistency of the Bayesian Estimator for the Ornstein–Uhlenbeck Process , 2014 .

[4] K. Elworthy. ERGODICITY FOR INFINITE DIMENSIONAL SYSTEMS (London Mathematical Society Lecture Note Series 229) By G. Da Prato and J. Zabczyk: 339 pp., £29.95, LMS Members' price £22.47, ISBN 0 521 57900 7 (Cambridge University Press, 1996). , 1997 .

[5] Arturo Kohatsu-Higa,et al. The Euler scheme for anticipating stochastic differential equations , 1995 .

[6] Thierry Jeantheau,et al. Stochastic volatility models as hidden Markov models and statistical applications , 2000 .

[7] N. Vayatis,et al. Strong Consistency of Bayesian Estimator Under Discrete Observations and Unknown Transition Density , 2011 .

[8] J. Zabczyk,et al. Ergodicity for Infinite Dimensional Systems: Invariant measures for stochastic evolution equations , 1996 .

[9] E. Gobet. LAN property for ergodic diffusions with discrete observations , 2002 .

[10] R. TUCKER,et al. The London Mathematical Society , 1900, Nature.

[11] Arturo Kohatsu-Higa,et al. High order Itô-Taylor approximations to heat kernels , 1997 .

[12] M. Sørensen,et al. CHAPTER 4 – Estimating Functions for Discretely Sampled Diffusion-Type Models , 2010 .