Parameter estimation in nonlinear stochastic differential equations

Parameter estimation in nonlinear stochastic dierential equations

We discuss the problem of parameter estimation in nonlinear stochastic di€erential equations (SDEs) based on sampled time series. A central message from the theory of integrating SDEs is that there exist in general two time scales, i.e. that of integrating these equations and that of sampling. We argue that therefore, maximum likelihood estimation is computationally extremely expensive. We disc...

Parameter Estimation in Stochastic Differential Equations

Financial processes as processes in nature, are subject to stochastic fluctuations. Stochastic differential equations turn out to be an advantageous representation of such noisy, real-world problems, and together with their identification, they play an important role in the sectors of finance, but also in physics and biotechnology. These equations, however, are often hard to represent and to re...

Parameter Estimation for Differential Equations

Estimation of Stochastic Differential Equations

The Stochastic differential equations, especially diffusion processes, have been widely used in physical and biological sciences and in financial economics. In mathematical finance the success of the diffusion process can be attributed to its many attractive properties. However, all models involve unknown parameters or functions, which need to be estimated from observations of the process. The ...

Parameter Estimation of Stochastic Differential Equation

Non-parametric modeling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline with Bayesian approach is considered in the first step of a two-step method in estimating the structural parameters for stochasti...