Diffusion processes, stochastic differential equations and applications

1995 ◽  
pp. 237-284
Author(s):  
Henry C. Tuckwell
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Diffusion Processes

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 Measure Diffusion Processes

1979 ◽  
Vol 22 (2) ◽  
pp. 129-138 ◽  
Author(s):  
Donald A. Dawson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Diffusion Processes ◽  
Partial Differential ◽  
Stochastic Measure ◽  
Recent Developments

The purpose of this article is to give an introduction to the study of a class of stochastic partial differential equations and to give a brief review of some of the recent developments in this field. This study has evolved naturally out of the theory of stochastic differential equations initiated in a pioneering paper of K. Itô [13]. In order to set this review in its appropriate setting we begin by considering a simple scalar stochastic differential equation.

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