File Name: feynman path integral discretization and its applications to nonlinear filtering .zip

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Published: 19.12.2020

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: The continuous-discrete filtering problem requires the solution of a partial differential equation known as the Fokker-Planck-Kolmogorov forward equation FPKfe. The path integral formula for the fundamental solution of the FPKfe is derived and verified for the general additive noise case i.

We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential. We propose a Fresnel stochastic white noise framework to analyze the nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under an external electromagnetic time-independent potential. Perfect discretization of path integrals. In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed.

Metrics details. In this paper, the Feynman path integral formulation of the continuous-continuous filtering problem, a fundamental problem of applied science, is investigated for the case when the noise in the signal and measurement model is Gaussian and additive. It is shown that it leads to an independent and self-contained analysis and solution of the problem. A consequence of this analysis is the configuration space Feynman path integral formula for the conditional probability density that manifests the underlying physics of the problem. A corollary of the path integral formula is the Yau algorithm that has been shown to have excellent numerical properties. The Feynman path integral formulation is shown to lead to practical and implementable algorithms. In particular, the solution of the Yau partial differential equation is reduced to one of function computation and integration.

Manuscript received September 13, ; final manuscript received November 6, ; published online January 27, Editor: John B. Morzfeld, M. January 27, May ; 5 : Implicit sampling is a recently developed variationally enhanced sampling method that guides its samples to regions of high probability, so that each sample carries information.

PDF | The continuous-discrete filtering problem requires the solution of a partial Universal Nonlinear Filtering Using Feynman Path Integrals I: The In a wide variety of applications, the evolution of a state, or a signal of interest, is described or the mid-point or Feynman discretization, agreement with the result obtained.

Information field theory IFT is a Bayesian statistical field theory relating to signal reconstruction , cosmography , and other related areas. It uses computational techniques developed for quantum field theory and statistical field theory to handle the infinite number of degrees of freedom of a field and to derive algorithms for the calculation of field expectation values. For example, the posterior expectation value of a field generated by a known Gaussian process and measured by a linear device with known Gaussian noise statistics is given by a generalized Wiener filter applied to the measured data. IFT extends such known filter formula to situations with nonlinear physics , nonlinear devices , non-Gaussian field or noise statistics, dependence of the noise statistics on the field values, and partly unknown parameters of measurement. For this it uses Feynman diagrams , renormalisation flow equations, and other methods from mathematical physics.

A study is required to see if the qPATHINT algorithm can scale sufficiently to further develop real-world calculations in these two systems, requiring interactions between classical and quantum scales. A new algorithm also is needed to develop interactions between classical and quantum scales. Both systems are developed using mathematical-physics methods of path integrals in quantum spaces. For the financial options study, all traded Greeks are calculated for Eurodollar options in quantum-money spaces. The mathematical-physics and computer parts of the study are successful for both systems. Each of the two systems considered contribute insight into applications of qPATHINT to the other system, leading to new algorithms presenting time-dependent propagation of interacting quantum and classical scales. Section 2 gives motivations for this proposed study.

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