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— In this paper the authors derive a new class of finite-dimensional recursive filters for linear dynamical systems. The Kalman filter is a special case of their general filter. Apart from being of mathematical interest, these new finite-dimensional filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of(More)
By analogy with the theory of Backward Stochastic Differential Equations , we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers properties of these processes as constructions in their own right, not as approximations to the continuous case. We establish the existence and(More)
In this paper, we derive a new class of finite-dimensional filters for integrals and stochastic integrals of moments of the state for continuous-time linear Gaussian systems. Apart from being of significant mathematical interest, these new filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of the model(More)
OBJECTIVES Non-alcoholic fatty liver disease (NAFLD) uncommonly results in cirrhosis and liver-related death; however, its impact on the development of metabolic complications remains unclear. We sought to determine whether NAFLD with elevated aminotransaminase (ALT) levels was a risk factor for incident diabetes or the metabolic syndrome (MS) over an(More)