Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition

1997 ◽  
Vol 33 (4) ◽  
pp. 1295-1308 ◽  
Author(s):  
Zhigang Liang ◽  
S.S.-T. Yau ◽  
S.T. Yau
Keyword(s):  
Kolmogorov Equation ◽  
Initial Condition ◽  
Linear Filtering ◽  
Finite Dimensional ◽  
Non Gaussian

scholarly journals Linear Filtering and Recursive Credibility Estimation

1985 ◽  
Vol 15 (1) ◽  
pp. 19-35 ◽  
Author(s):  
Ben Zehnwirth
Keyword(s):  
Geometric Interpretation ◽  
Linear Filtering ◽  
Filtering Theory ◽  
Innovation Approach ◽  
Non Gaussian

AbstractRecursive credibility estimation is discussed from the viewpoint of linear filtering theory. A conjunction of geometric interpretation and the innovation approach leads to general algorithms not developed before. Moreover, covariance characterizations considered by other researchers drop our elegantly as a result of geometric considerations. Examples are presented of Kalman type filters valid for non-Gaussian measurements.

Finite-dimensional models for hidden Markov chains

1995 ◽  
Vol 27 (01) ◽  
pp. 146-160
Author(s):  
Lakhdar Aggoun ◽  
Robert J. Elliott
Keyword(s):  
Markov Chains ◽  
Expectation Maximization ◽  
Continuous Time ◽  
Hidden Markov ◽  
Expectation Maximization Algorithm ◽  
Linear Filtering ◽  
Occupation Times ◽  
Finite Dimensional ◽  
Self Tuning ◽  
Filtering Problem

A continuous-time, non-linear filtering problem is considered in which both signal and observation processes are Markov chains. New finite-dimensional filters and smoothers are obtained for the state of the signal, for the number of jumps from one state to another, for the occupation time in any state of the signal, and for joint occupation times of the two processes. These estimates are then used in the expectation maximization algorithm to improve the parameters in the model. Consequently, our filters and model are adaptive, or self-tuning.

scholarly journals SMOOTH PROBABILITY MEASURES AND ASSOCIATED DIFFERENTIAL OPERATORS

1999 ◽  
Vol 02 (01) ◽  
pp. 51-78 ◽  
Author(s):  
O. G. SMOLYANOV ◽  
H. v. WEIZSÄCKER
Keyword(s):  
Differential Operators ◽  
Finite Dimensional ◽  
Differentiable Measure ◽  
Chaos Decomposition ◽  
Gaussian Case ◽  
Non Gaussian ◽  
Associated Differential Operators ◽  
Locally Convex ◽  
Nonsmooth Mappings

We compare different notions of differentiability of a measure along a vector field on a locally convex space. We consider in the L2-space of a differentiable measure the analog of the classical concepts of gradient, divergence and Laplacian (which coincides with the Ornstein–Uhlenbeck operator in the Gaussian case). We use these operators for the extension of the basic results of Malliavin and Stroock on the smoothness of finite dimensional image measures under certain nonsmooth mappings to the case of non-Gaussian measures. The proof of this extension is quite straight forward and does not use any Chaos-decomposition. Finally, the role of this Laplacian in the procedure of quantization of anharmonic oscillators is discussed.

Identification of Non-Gaussian Stochastic System

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Sung-man Park ◽  
O-shin Kwon ◽  
Jin-sung Kim ◽  
Jong-bok Lee ◽  
Hoon Heo
Keyword(s):  
Random Process ◽  
Random Noise ◽  
Stochastic Simulations ◽  
Kolmogorov Equation ◽  
Gaussian Random Process ◽  
System Parameters ◽  
Analysis Technique ◽  
Gaussian Analysis ◽  
Gaussian System ◽  
Non Gaussian

This paper proposes a method to identify non-Gaussian random noise in an unknown system through the use of a modified system identification (ID) technique in the stochastic domain, which is based on a recently developed Gaussian system ID. The non-Gaussian random process is approximated via an equivalent Gaussian approach. A modified Fokker–Planck–Kolmogorov equation based on a non-Gaussian analysis technique is adopted to utilize an effective Gaussian random process that represents an implied non-Gaussian random process. When a system under non-Gaussian random noise reveals stationary moment output, the system parameters can be extracted via symbolic computation. Monte Carlo stochastic simulations are conducted to reveal some approximate results, which are close to the actual values of the system parameters.

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