Related papers: On Lamperti transformation and characterisations o…
In the paper we consider Lamperti type theorems for random fields. Together with known results we present some new results on ${\mathbb R}^m$-valued self-similar fields $\{{\bf X} ({\bf t}), \ {\bf t} \in {\mathbb R}^d \}$, their domains of…
In this article, we consider three important classes of $n$-variate fields indexed by the set of $N$ dimensional integers, namely stationary, stationary increment and self-similar fields. These classes are connected through bijective…
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 describe two classes of Gaussian self-similar random fields: with strictly stationary rectangular increments and with mild stationary rectangular increments. We find explicit spectral and moving average representations for the fields…
This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average fields…
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…
In this article, we characterize continuous stationary fields via generalized Langevin dynamics. This gives natural connections between stationary fields, stationary increment fields, self-similar fields, and generalized Langevin dynamics.…
We introduce a novel method for estimating the self-similarity index of a general $H$-self-similar process with either stationary or non-stationary increments. The estimation algorithm is developed based on a modified Lamperti…
We are interested in the increment stationarity property for $L^2$-indexed stochastic processes, which is a fairly general concern since many random fields can be interpreted as the restriction of a more generally defined $L^2$-indexed…
We analyze certain stationary fields with linear regressions and quadratic conditional variances. This classic probabilistic problem leads somewhat unexpectedly to stationary Markov processes closely tied to non-commutative probability…
In the paper we present simple examples of linear random fields defined on $\ZZ^2$ and $\ZZ^3$ which exhibit the scaling transition phenomenon. These examples lead to more general definition of the scaling transition and allow to understand…
The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known on the context…
Mixed moving average processes appear in the ergodic decomposition of stationary symmetric \alpha-stable (S\alpha S) processes. They correspond to the dissipative part of "deterministic" flows generating S\alpha S processes (Rosinski,…
In this paper we study the local times of vector-valued Gaussian fields that are `diagonally operator-self-similar' and whose increments are stationary. Denoting the local time of such a Gaussian field around the spatial origin and over the…
In this paper, we give a AR$(1)$ type of characterization covering all multivariate strictly stationary processes indexed by the set of integers. Consequently, we derive continuous time algebraic Riccati equations for the parameter matrix…
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…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
The paper investigates properties of generalized Hermite-type processes that arise in non-central limit theorems for integral functionals of long-range dependent random fields. The case of increasing multidimensional domain asymptotics is…
Dilative stability generalizes the property of selfsimilarity for infinitely divisible stochastic processes by introducing an additional scaling in the convolution exponent. Inspired by results of Igl\'oi, we will show how dilatively stable…
We introduce a classical field theory based on a concept of extended causality that mimics the causality of a point-particle Classical Mechanics by imposing constraints that are equivalent to a particle initial position and velocity. It…