ShinIchi Aihara

Estimation of stochastic volatility in the Hull-White model

Estimation of the stochastic volatility in the Hull-White framework is considered. Stock price is taken as the observation and the estimation problem is posed for the stochastic volatility. It is first shown that it is not possible to formulate this as the usual filtering problem, and an alternative formulation is proposed. A robust filtering equation is then derived suitable for real observation data.

Parameter identification for stochastic diffusion equations with unknown boundary conditions

Stochastic diffusion equations with unknown boundary conditions are encountered in practice whenever the boundary is observed only through measurement errors. Parameter identification for such systems is studied in the present paper. The boundary condition is treated as an unknown parameter in a function space as an intermediate step in solving the identification problem.

Consistency property of extended least-squares parameter estimation for stochastic diffusion equation

The extended least-squares parameter estimate for stochastic heat diffusion equations is considered. The unknown parameter is a heat diffusion coefficient which is a function of a spatial variable. Almost sure convergence for the estimated parameter is proved. A numerical example is demonstrated for supporting the theoretical results developed here.

On the finite time stability for stochastic distributed parameter systems with free boundary-application to the micro-tunneling machine

We consider a finite-time stochastic stability for distributed parameter systems with free boundary condition. This mathematical model is deduced from the analysis of the tracking error of the installed pipe from the designed path in the micro-tunneling machine. After showing that the proposed mathematical system has a solution in some function spaces, we study the finite-time stability problem. The buckling phenomena of the installed pipe is simulated related to the derived sufficient conditions for the finite-time stability.

Asymptotic behavior of the minimum energy filter as a recursive parameter estimator

By introducing an energy cost for an estimator whose form is a-priori set, we can derive an optimal estimator for the argumentative state of the system state and unknown parameters. The asymptotic behavior of the estimate is studied. Some numerical examples are demonstrated.

Identification of objects of complex shape by using stochastic local fractal variables–categorizing dust particles on lsi wafer surface

When a natural object or phenomenon is modelled mathematically by using a fractal dimension, it is recognized that the object or phenomenon does not often have an autocorrelation. In the fractal theory, a fractal dimension is defined as a determined value (dimension) which is independent of the scale of its covering. In practice, however, the dimension often fluctuates depending on samples used (even with the same object or phenomenon) and its scale. In published works of image analyses using fractal dimensions, it has been assumed that fractal dimensions are determined and independent of scales, ignoring the practical experience. To treat a natural object or phenomenon without contradictions, this paper introduces “stochastic local fractal variables.” Using these new variables, mathematical models of dust on LSI wafers are constructed, and they are identified by using the likelihood method. Usefulness of the proposed method has successfully been confirmed with real data.

Identification for complicated shape objects by using stochastic fractal variables—categorizing dust particles on LSI wafer surface

Improving the yield and stability of LSI wafer production requires that the number of dust particles during every process of the production be decreased. To do this, we must develop a method of identifying dust particles. However, the current method of inspecting LSI wafers depends on human judgment; this makes it difficult to develop an algorithm to identify dust particles with complex shapes because mathematical models of dust particles have not been created. With this study, we propose the so-called “stochastic fractal variable” to make the mathematical model and identify the dust particles by using the maximum-likelihood method. Furthermore, we confirm the effectiveness of the identification method we propose by categorizing actual data.

Linear-quadratic stochastic differential games for distributed parameter systems

A linear-quadratic differential game with infinite dimensional state space is considered. The system state is affected by disturbance and both players have access to different measurements. Optimal linear strategies for the pursuer and the evader, when they exist, are explicitly determined.

On the state estimation for stochastic distributed parameter systems with the boundary regulation

This paper is concerned with the state estimation problem for the stochastic distributed parameter systems with the boundary regulation. Formulating the system model as a stochastic variational inequality, the existence and uniqueness properties of the solution are investigated. The dynamics of the state estimator is given under a distributed observation mechanism. For the purpose of supporting the theoretical aspects developed here, an illustrative example is shown including results of digital simulation experiments.

Parameter identification for stochastic diffusion equations with unkown boundary conditions

Stochastic diffusion equations with unknown boundary conditions are encountered in practice whenever the boundary is observed only through measurement errors. Parameter identification for such systems is studied in the present paper. Boundary condition is treated as an unknown parameter in a function space as an intermediate step in solving the identification problem.