相关论文: Universal Nonlinear Filtering Using Feynman Path I…
We consider the thermally activated escape of an overdamped Brownian particle over a potential barrier in the presence of periodic driving. A time-dependent path-integral formalism is developed which allows us to derive asymptotically exact…
In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's…
We give meaning to differential equations with a rough path term and a Brownian noise term as driving signals. Such differential equations as well as the question of regularity of the solution map arise naturally and we discuss two…
In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we…
One of the key elements of Feynman's formulation of non-relativistic quantum mechanics is a so-called Feynman path integral. It plays an important role in the theory, but it appears as a postulate based on intuition rather than a…
In this paper, we propose an approach to address the problems with ambiguity in tuning the process and observation noises for a discrete-time linear Kalman filter. Conventional approaches to tuning (e.g. using normalized estimation error…
Feynman path integrals provide an elegant, classically inspired representation for the quantum propagator and the quantum dynamics, through summing over a huge manifold of all possible paths. From computational and simulational…
We derive the path-integral representation of the fractional Ornstein-Uhlenbeck process driven by Riemann-Liouville fractional Gaussian noise, for both the subdiffusive and superdiffusive regimes. We express the corresponding action, which…
The Feynman path integral approach to quantum mechanics is examined in the case where the configuration space is curved. It is shown how the ambiguity that is present in the choice of path integral measure may be resolved if, in addition to…
When employing Feynman path integrals to compute propagators in quantum physics, the concept of summing over the set of all paths is not always naive. In fact, an auxiliary phase often has to be included as a weight for each summand. In…
Integrated Gradients (IG) is a commonly used feature attribution method for deep neural networks. While IG has many desirable properties, the method often produces spurious/noisy pixel attributions in regions that are not related to the…
The Feynman path integral approach for computing equilibrium isotope effects and isotope fractionation corrects the approximations made in standard methods, although at significantly increased computational cost. We describe an accelerated…
We construct a pathwise integration theory, associated with a change of variable formula, for smooth functionals of continuous paths with arbitrary regularity defined in terms of the notion of $p$-th variation along a sequence of time…
This article develops a methodology allowing application of the complete machinery of particle-based inference methods upon the class of continuous-discrete State Space Models (CD-SSMs). Such models correspond to a latent continuous-time…
The paper provides simple formulas of Bayesian filtering for the exact recursive computation of state conditional probability density functions given quantized innovations signal measurements of a linear stochastic system. This is a topic…
This paper proposes new algorithms for attitude estimation and control based on fused inertial vector measurements using linear complementary filters principle. First, n-order direct and passive complementary filters combined with TRIAD…
The particle filter is one of the most successful methods for state inference and identification of general non-linear and non-Gaussian models. However, standard particle filters suffer from degeneracy of the particle weights, in particular…
We present an analysis of the Feynman path centroid density that provides new insight into the correspondence between the path integral and the Schr\"odinger formulations of statistical mechanics. The path centroid density is a central…
A fully regulated definition of Feynman's path integral is presented here. The proposed re-formulation of the path integral coincides with the familiar formulation whenever the path integral is well-defined. In particular, it is consistent…
Feynman proposed a postulate or a method of quantization in his celebrated paper in 1948. Applying Feynman's postulate to temporally continuous quantum measurements of the positions of particles, Mensky proposed the restricted Feynman path…