Parameter Estimation of Nonlinear Stochastic Differential Equations: Simulated Maximum Likelihood versus Extended Kalman Filter and Itô-Taylor Expansion

2002 ◽  
Vol 11 (4) ◽  
pp. 972-995 ◽  
Author(s):  
Hermann Singer
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Maximum Likelihood ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Extended Kalman Filter ◽  
Taylor Expansion ◽  
Simulated Maximum Likelihood ◽  
Nonlinear Stochastic Differential Equations

On effects of discretization on estimators of drift parameters for diffusion processes

1996 ◽  
Vol 33 (04) ◽  
pp. 1061-1076 ◽  
Author(s):  
P. E. Kloeden ◽  
E. Platen ◽  
H. Schurz ◽  
M. Sørensen
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Numerical Methods ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Diffusion Processes ◽  
Maximum Likelihood Estimators ◽  
Statistical Properties ◽  
Stochastic Integrals

In this paper statistical properties of estimators of drift parameters for diffusion processes are studied by modern numerical methods for stochastic differential equations. This is a particularly useful method for discrete time samples, where estimators can be constructed by making discrete time approximations to the stochastic integrals appearing in the maximum likelihood estimators for continuously observed diffusions. A review is given of the necessary theory for parameter estimation for diffusion processes and for simulation of diffusion processes. Three examples are studied.

On effects of discretization on estimators of drift parameters for diffusion processes

1996 ◽  
Vol 33 (4) ◽  
pp. 1061-1076 ◽  
Author(s):  
P. E. Kloeden ◽  
E. Platen ◽  
H. Schurz ◽  
M. Sørensen
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Numerical Methods ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Diffusion Processes ◽  
Maximum Likelihood Estimators ◽  
Statistical Properties ◽  
Stochastic Integrals

In this paper statistical properties of estimators of drift parameters for diffusion processes are studied by modern numerical methods for stochastic differential equations. This is a particularly useful method for discrete time samples, where estimators can be constructed by making discrete time approximations to the stochastic integrals appearing in the maximum likelihood estimators for continuously observed diffusions. A review is given of the necessary theory for parameter estimation for diffusion processes and for simulation of diffusion processes. Three examples are studied.

A new numerical method for 1-D backward stochastic differential equations without using conditional expectations

2020 ◽  
Vol 28 (2) ◽  
pp. 79-91
Author(s):  
Aissa Sghir ◽  
Sokaina Hadiri
Keyword(s):  
Kalman Filter ◽  
Linear System ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Extended Kalman Filter ◽  
Backward Stochastic Differential Equations ◽  
Conditional Expectations ◽  
Non Linear System ◽  
Reference Trajectories

AbstractIn this paper, we propose a new numerical method for 1-D backward stochastic differential equations (BSDEs for short) without using conditional expectations. The approximations of the solutions are obtained as solutions of a backward linear system generated by the terminal conditions. Our idea is inspired from the extended Kalman filter to non-linear system models by using a linear approximation around deterministic nominal reference trajectories.

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