On Guaranteed Parameter Estimation of Stochastic Delay Differential Equations by Noisy Observations

Lipari 2009 Biomathematics Summer School. Parameter Estimation in Physiological Models. Parameter Estimation for Stochastic Differential Equations from Noisy Observations. Maximum Likelihood and Filtering Techniques

On sequential parameter estimation of a linear regression process ?

This paper presents a sequential estimation procedure for unknown parameters of a stochastic linear regression. As examples the sequential estimation problem of two dynamic parameters in stochastic linear systems with memory and in autoregressive processes is solved. The estimation procedure is based on the least squares method with weights and yields estimators with guaranteed accuracy in the ...

Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

On guaranteed parameter estimation of a multiparameter linear regression process

This paper presents a sequential estimation procedure for the unknown parameters of a continuous-time stochastic linear regression process. As examples the sequential estimation problem of two dynamic parameters in stochastic linear systems with memory and in autoregressive processes is solved. The estimation procedure is based on the least squares method with weights and yields estimators with...

Computational Method for Fractional-Order Stochastic Delay Differential Equations

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...