Gaussian behavior, process parameters

The model described in Brennan and Schwartz (1979) uses the short rate and the long-term interest rate to specify the term structure. The long-term rate is defined as the market yield on an irredeemable, or perpetual, bond, also known as an undated or consol bond. Both interest rates are assumed to follow a Gaussian-Markov process. A Gaussian process is one whose marginal distribution, where parameters are random variables, displays normal distribution behavior a Markov process is one whose future behavior is conditional on its present behavior only, and independent of its past. A later study, Longstaff and Schwartz (1992), found that Brennan-Schwartz modeled market bond yields accurately. 

Although the polymer chains must possess chemical specificity in order to express their unique functions in various macromolecular processes, they exhibit certain universal behavior at larger length scales. By parametrizing the chemical details at the monomeric level, we have described various coarsegrained models, namely the Kuhn chain, Gaussian chain, and the wormlike Kratky-Porod chain. Chain stiffness is captured by the persistence length parameter. 

A Gaussian, process noise level of 0.1 % RMS noise-to-signal ratio is assumed, while the observation noise corresponds to approximately 10 % RMS. No process noise is added for the time-invariant parameter components. The addition of some minor noise could improve parameter estimation for the PF however, it might also lead to instabilities and non-converging behavior. The observation noise is chosen so as to reflect a realistic instrumentation noise level, whereas the process noise is kept to a low level indicating confidence that the observed system can be described by this type of a model formulation. 

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