9 papers
Bayesian Filters via the Stochastic Category
Kenichi Bannai, Masahiro Kurisaki
We extend the categorical treatment of Bayesian filters to models with feedback, whose transitions and observations may depend on the past observations. We work in the stochastic c…
Finite Cumulant Towers for Small-System-Noise Expansions in Nonlinear Filtering
Masahiro Kurisaki
We study asymptotic expansions for nonlinear filtering in the small-system-noise regime. Our main result is that the expansion coefficients of conditional cumulants satisfy a close…
A Second-Order Asymptotic Expansion for Nonlinear Filtering in the Lorenz--63 System
Masahiro Kurisaki, Kota Takeda
A challenge in nonlinear filtering is to incorporate nonlinear effects into approximations of the conditional mean while retaining a finite-dimensional recursive algorithm. We deri…
Finite-Dimensional Recursions for Small-Noise Expansions in Nonlinear Filtering
Masahiro Kurisaki
This paper provides a recursive formula for computing the coefficients in a small-system-noise asymptotic expansion for nonlinear filtering. The expansion, obtained from the Kallia…
Asymptotic Expansion of the Kallianpur-Striebel Formula under Perturbations of Linear Models
Masahiro Kurisaki
In this paper, we study a nonlinear state-space model represented as a perturbation of a linear model and investigate an asymptotic expansion of the nonlinear filter with respect t…
Pathwise Representation of the Smoothing Distribution in Continuous-Time Linear Gaussian Models
Masahiro Kurisaki
We study the filtering and smoothing problem for continuous-time linear Gaussian systems. While classical approaches such as the Kalman-Bucy filter and the Rauch-Tung-Striebel (RTS…
Asymptotic Expansion for Nonlinear Filtering in the Small System Noise Regime
Masahiro Kurisaki
We propose a new asymptotic expansion method for nonlinear filtering, based on a small parameter in the system noise. The conditional expectation is expanded as a power series in t…
A New Proof for the Linear Filtering and Smoothing Equations, and Asymptotic Expansion of Nonlinear Filtering
Masahiro Kurisaki
In this paper, we propose a new asymptotic expansion approach for nonlinear filtering based on a small parameter in the system noise. This method expresses the filtering distributi…
Parameter estimation for ergodic linear SDEs from partial and discrete observations
Masahiro Kurisaki
We consider a problem of parameter estimation for the state space model described by linear stochastic differential equations. We assume that an unobservable Ornstein-Uhlenbeck pro…