Related papers: Characterization of unitary processes with indepen…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
We analyze a jump processes $Z$ with a jump measure determined by a "memory" process $S$. The state space of $(Z,S)$ is the Cartesian product of the unit circle and the real line. We prove that the stationary distribution of $(Z,S)$ is the…
Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…
By means of the unitary transformation, a new way for discussing the ordering prescription of Schrodinger equation with a position-dependent mass (PDM) for isospectral Hamiltonian operators is presented. We show that the ambiguity parameter…
In this Letter, we interpret the Husimi function as the conditional probability density of continuously measuring a stream of constant position and momentum outcomes, indefinitely. This gives rise to an alternative definition that naturally…
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…
We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral…
In quantum logical terms, Hardy-type arguments can be uniformly presented and extended as collections of intertwined contexts and their observables. If interpreted classically those structures serve as graph-theoretic "gadgets" that enforce…
This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on $d$-variate random vectors ($d\geq1$). First, a uniform Gaussian strong approximation is established for general…
We consider the winding number of planar stationary Gaussian processes defined on the line. Under mild conditions, we obtain the asymptotic variance and the Central Limit Theorem for the winding number as the time horizon tends to infinity.…
We study point processes on the real line whose configurations $X$ are locally finite, have a maximum and evolve through increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and…
\noindent The paper establishes weak convergence in $C[0,1]$ of normalized stochastic processes, generated by Toeplitz type quadratic functionals of a continuous time Gaussian stationary process, exhibiting long-range dependence. Both…
We introduce an index based on information theory to quantify the stationarity of a stochastic process.The index compares on the one hand the information contained in the increment at the time scale $\tau$ of the process at time $t$ with,…
The analytic properties of the elastic hadron scattering amplitude are examined in the impact parameter representation at high energies. Different unitarization procedures and the corresponding non-linear equations are presented. Several…
The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…
We study which standard operators of probabilistic process calculi allow for compositional reasoning with respect to bisimulation metric semantics. We argue that uniform continuity (generalizing the earlier proposed property of…
We present the time dynamics of twisted quantum states. We find an explicit connection between the well-known stationary Landau state and an evolving twisted state, even when the Hamiltonian accounts for linear energy dissipation. Utilizing…
Landauer's principle, a cornerstone of quantum information and thermodynamics, appears to be violated when the thermal reservoir is replaced by a squeezed thermal state (STS), owing to the additional thermodynamic resources inherently…
This paper proposes a new approach to obtain uniformly valid inference for linear functionals or scalar subvectors of a partially identified parameter defined by linear moment inequalities. The procedure amounts to bootstrapping the value…
We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses.…