scholarly journals On parameter identification in stochastic differential equations by penalized maximum likelihood

2014 ◽  
Vol 30 (9) ◽  
pp. 095001 ◽  
Author(s):  
Fabian Dunker ◽  
Thorsten Hohage
Keyword(s):  
Maximum Likelihood ◽  
Differential Equations ◽  
Parameter Identification ◽  
Stochastic Differential Equations ◽  
Penalized Maximum Likelihood

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.

scholarly journals Stochastic Analysis of Gaussian Processes via Fredholm Representation

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Tommi Sottinen ◽  
Lauri Viitasaari
Keyword(s):  
Brownian Motion ◽  
Maximum Likelihood ◽  
Differential Equations ◽  
Gaussian Process ◽  
Stochastic Differential Equations ◽  
Gaussian Processes ◽  
Stochastic Analysis ◽  
Series Expansions ◽  
Transfer Principle ◽  
Maximum Likelihood Estimations

We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic analysis by using it. We show the convenience of the Fredholm representation by giving applications to equivalence in law, bridges, series expansions, stochastic differential equations, and maximum likelihood estimations.

Parameter Identification in Stochastic Differential Equations to Model the Degradation of Metal Films

PAMM ◽  
2017 ◽  
Vol 17 (1) ◽  
pp. 775-776 ◽  
Author(s):  
Barbara Pedretscher ◽  
Barbara Kaltenbacher ◽  
Olivia Bluder
Keyword(s):  
Differential Equations ◽  
Parameter Identification ◽  
Stochastic Differential Equations ◽  
Metal Films

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.

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