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- W2943545703 abstract "Path integral has been found to be useful as a way to study stochastic processes such as filtering and control. However, it is not clear how to directly define the path integral itself as a probability density for the stochastic processes in the perspective of physics. This paper proposes weighted distribution in discrete-time stochastic quantization to describe nonlinear stochastic processes on filtering and control. Although the weighted distribution has been considered in fields on statistics, we explain that the weighted distribution gives the path integral additional potentials while preserving as a role of probability density for the path integral. We construct explicit models on Extended Kalman filter, Extended Kalman filter with a constraint and a nonlinear stochastic control model for the suitable weighted distributions. It is typical in nonlinear filtering that observations assume the existence of the corresponding probability density. In our model, we point out that the potential involves the observations as external sources which do not require the probability density. While backward equations are used for typical control models, the nonlinear control model is described by forward difference equations in our model. A control variable is naturally given as a force induced from the potentials. The numerical simulations show that Langevin equation can be controlled towards a target value given by a local minimum of the potential." @default.
- W2943545703 created "2019-05-09" @default.
- W2943545703 creator A5028816027 @default.
- W2943545703 date "2019-05-04" @default.
- W2943545703 modified "2023-09-27" @default.
- W2943545703 title "Stochastic quantization with Weighted distribution in discrete time for Filtering and Control." @default.
- W2943545703 hasPublicationYear "2019" @default.
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