Related papers: Unitary Processes with Independent Increments
This is a continuation of the earlier work \cite{SSS} to characterize stationary unitary increment Gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with a technical assumption on the domain…
The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow.
Stationary stochastic processes with independent increments, of which the Poisson process is a prominent example, are widely used to describe real world events. With the basic assumption that a counting process is stationary and has…
We show that the Hadamard and Unitary gates could be implemented by a unitary evolution together with a measurement for any unknown state chosen from a set $A = {{| {\Psi_i} > ,| {\bar {\Psi}_i} >}}({i = 1,2})$ if and only if $| {\Psi_1} >…
We define a new matrix-valued stochastic process with independent stationary increments from the Laguerre Unitary Ensemble, which in a certain sense may be considered a matrix generalisation of the gamma process. We show that eigenvalues of…
We describe all countable particle systems on $\mathbb{R}$ which have the following three properties: independence, Gaussianity and stationarity. More precisely, we consider particles on the real line starting at the points of a Poisson…
New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of nonstationary processes. An application of the…
In this paper we study three self-similar, long-range dependence, Gaussian processes. The first one, with covariance \int_0^{s\wedge t} u^a [(t-u)^b+(s-u)^b]du, parameters a>-1, -1<b\leq 1, |b|\leq 1+a, corresponds to fractional Brownian…
In this article we prove large deviations principles for high minima of Gaussian processes with nonnegatively correlated increments on arbitrary intervals. Furthermore, we prove large deviations principles for the increments of such…
In this paper we study the self-similar processes with stationary increments in a discrete-time setting. Different from the continuous-time case, it is shown that the scaling function of such a process may not take the form of a power…
Our purpose is to investigate properties for processes with stationary and independent increments under $G$-expectation. As applications, we prove the martingale characterization to $G$-Brownian motion and present a decomposition for…
In this article we characterise discrete time stationary fields by difference equations involving stationary increment fields and self-similar fields. This gives connections between stationary fields, stationary increment fields and,…
Random processes with stationary increments and intrinsic random processes are two concepts commonly used to deal with non-stationary random processes. They are broader classes than stationary random processes and conceptually closely…
We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures sigma (generalized spectral measures), and our focus here is on the case when the measure sigma is a singular…
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent…
The goal of this paper is to establish a relation between characteristic polynomials of $N\times N$ GUE random matrices $\mathcal{H}$ as $N\to\infty$, and Gaussian processes with logarithmic correlations. We introduce a regularized version…
We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H>1/2 as a typical example. We establish infinite and finite past…
We prove one-to-one correspondences between certain decreasing Loewner chains in the upper half-plane, a special class of real-valued Markov processes, and quantum stochastic processes with monotonically independent additive increments.…
The Lamperti transform offers a powerful bridge between self-similar processes and stationary dynamics, making it especially useful for analyzing anomalous diffusion models that lack stationary increments. In this paper we examine the…
We consider $d$-dimensional quantum systems which for positive times evolve with a time-independent Hamiltonian in a nonequilibrium state that we keep generic in order to account for arbitrary evolution at negative times. We show how the…