Related papers: Wiener integrals with respect to the two-parameter…
In this work, we investigate a theory of stochastic integration for operator-valued processes with respect to semimartingales taking values in the dual of a nuclear space. Our construction of this particular stochastic integral relies on…
In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristic of the function's persistent homology. We then proceed to…
The paper contains an exposition of recent as well as old enough results on determinantal random point fields. We start with some general theorems including the proofs of the necessary and sufficient condition for the existence of the…
I--MR charts commonly estimate the process standard deviation $\sigma$ via the span-2 average moving range divided by the unbiasing constant $d_2$; unlike the unbiased sample standard deviation ($S/c_4$), this estimator depends on ordering…
We give a simple proof of the Kernel theorem for the space of tempered ultradistributions of Beurling - Komatsu type, using the characterization of Fourier-Hermite coefficients of the elements of the space. We prove in details that the test…
We prove that in bosonic quantum mechanics the two-point spectral form factor can be obtained as an average of the two-point out-of-time ordered correlation function, with the average taken over the Heisenberg group. In quantum field…
A normal ordered exponential parametrization is used to obtain equations for thermal one-and two-particle reduced density matrices, as well as free energies, partition functions and entropy for both Fermionic (electronic) and Bosonic…
The article is devoted to the expansions of iterated Ito stochastic integrals based on generalized multiple Fourier series converging in the sense of norm in the space $L_2([t, T]^k),$ $k\in\mathbb{N}.$ The method of generalized multiple…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
The classical Wiener-Khinchin theorem (WKT), which can extract spectral information by classical interferometers through Fourier transform, is a fundamental theorem used in many disciplines. However, there is still need for a quantum…
In various applications of heavy-tail modelling, the assumed Pareto behavior is tempered ultimately in the range of the largest data. In insurance applications, claim payments are influenced by claim management and claims may for instance…
We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effective dynamics solves a rough differential equation, which is…
We report a phase transition in the projected ensemble - the collection of post-measurement wavefunctions of a local subsystem obtained by measuring its complement. The transition emerges in systems undergoing random permutation dynamics, a…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
Simulated tempering is popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. One problem with simulated tempering for multimodal targets is that the weights of the various modes change for…
This article consists of two parts. The main objectives of Part 1 are to postulate a new principle of representation invariance (PRI), and to refine the unified field model of four interactions, derived using the principle of interaction…
We propose a Bayesian semiparametric approach for registration of multiple point processes. Our approach entails modelling the mean measures of the phase-varying point processes with a Bernstein-Dirichlet prior, which induces a prior on the…
For a quantum system undergoing a unitary process work is commonly defined based on the Two Projective Measurement (TPM) protocol which measures the energies of the system before and after the process. However, it is well known that…
A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and the Weinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling…
Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two…