相关论文: The Clark-Ocone formula for vector valued random v…

Earlier work presented a spacetime path formalism for relativistic quantum mechanics arising naturally from the fundamental principles of the Born probability rule, superposition, and spacetime translation invariance. The resulting…

In Monte Carlo calculations of expectation values in lattice quantum field theories, the stochastic variance of the sampling procedure that is used defines the precision of the calculation for a fixed number of samples. If the variance of…

We establish a general CCR (liminarity) property for uniformly bounded irreducible representations of nilpotent Lie groups on reflexive Banach spaces, extending the well known property of unitary irreducible representations of these groups…

An iterative randomness extraction algorithm which generalized the Von Neumann's extraction algorithm is detailed, analyzed and implemented in standard C++. Given a sequence of independently and identically distributed biased Bernoulli…

The Nevanlinna transform K(z), of a measure and a real constant, plays an important role in the complex analysis and more recently in the free probability theory (boolean convolution). It is shown that its restriction k(it) (the restricted…

The commutator between operators at different space and time has been a diagnostic for locality of unitary evolution. Most existing results are either for specific tractable (random) Hamiltonians(Out-of-Time-Order-Correlators calculations),…

We express covariance of the Batalin-Vilkovisky formalism in classical mechanics by means of the Maurer-Cartan equation in a curved Lie superalgebra, defined using the formal variational calculus and Sullivan's Thom-Whitney construction. We…

We establish a direct connection between the Feynman-Vernon path integral formalism for open quantum systems and the Wiener path integral used in classical stochastic dynamics. By considering a generalized influence functional in the strong…

Two-way relationships between transformations and quadratic forms on Wiener spaces are investigated with the help of change of variables formulas on Wiener spaces. Further the evaluation of Laplace transforms of quadratic forms via Riccati…

We establish a framework for oracle identification problems in the continuous variable setting, where the stated problem necessarily is the same as in the discrete variable case, and continuous variables are manifested through a continuous…

We present a novel family of continuous, linear time-frequency transforms adaptable to a multitude of (nonlinear) frequency scales. Similar to classical time-frequency or time-scale representations, the representation coefficients are…

The model considered is that of ``signal plus white noise.'' Known connections between the noncausal filtering error and mutual information are combined with new ones involving the causal estimation error, in a general abstract setup. The…

In this letter we propose to use an extension of the variational approach known as Truncated Conformal Space to compute numerically the Vacuum Expectation Values of the operators of a conformal field theory perturbed by a relevant operator.…

We construct a covariant version of the Tolman-Oppenheimer-Volkoff equations in the case of isotropic sources. The new equations make evident the mathematical problems in the determination of interior solutions of relativistic stellar…

Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…

In 1998, Bou\'e and Dupuis proved a variational representation for exponentials of bounded Wiener functionals. Since their proof involves arguments related to the weak convergence of probability measures, the boundedness of functionals…

Misclassified variables used in regression models, either as a covariate or as the response, may lead to biased estimators and incorrect inference. Even though Bayesian models to adjust for misclassification error exist, it has not been…

The Clark-Ocone formula in the theory of discrete-time chaotic calculus holds only for square integrable functionals of discrete-time normal noises. In this paper, we aim at extending this formula to generalized functionals of discrete-time…

This article considers linear processes with values in a separable Hilbert space exhibiting long-range dependence. The scaling limits for the sample autocovariance operators at different time lags are investigated in the topology of their…

Generalizable implicit neural representation (INR) enables a single continuous function, i.e., a coordinate-based neural network, to represent multiple data instances by modulating its weights or intermediate features using latent codes.…