Stochastic Integrals and Differential Equations

2004 ◽  
pp. 53-65
Author(s):  
Jürgen Franke ◽  
Wolfgang Härdle ◽  
Christian M. Hafner
Keyword(s):  
Differential Equations ◽  
Stochastic Integrals

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 Integrals and Conditional Full Support

2010 ◽  
Vol 47 (03) ◽  
pp. 650-667 ◽  
Author(s):  
Mikko S. Pakkanen
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Volatility ◽  
Additional Assumption ◽  
Continuous Process ◽  
Stochastic Integrals ◽  
Finite Variation ◽  
Stochastic Volatility Models ◽  
Full Support ◽  
Volatility Models

We present conditions that imply the conditional full support (CFS) property, introduced in Guasoni, Rásonyi and Schachermayer (2008), for processes Z := H + ∫K dW, where W is a Brownian motion, H is a continuous process, and processes H and K are either progressive or independent of W. Moreover, in the latter case, under an additional assumption that K is of finite variation, we present conditions under which Z has CFS also when W is replaced with a general continuous process with CFS. As applications of these results, we show that several stochastic volatility models and the solutions of certain stochastic differential equations have CFS.

Stochastic Integrals and Differential Equations

2012 ◽  
pp. 43-58
Author(s):  
Szymon Borak ◽  
Wolfgang Karl Härdle ◽  
Brenda López-Cabrera
Keyword(s):  
Differential Equations ◽  
Stochastic Integrals
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