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We construct a class of nonnegative martingale processes that oscillate indefinitely with high probability. For these processes, we state a uniform rate of the number of oscillations and show that this rate is asymptotically close to the…
Automata expressiveness is an essential feature in understanding which of the formalisms available should be chosen for modelling a particular problem. Probabilistic and stochastic automata are suitable for modelling systems exhibiting…
This paper concerns applications of variational analysis to some local aspects of behavioral science modeling by developing an effective variational rationality approach to these and related issues. Our main attention is paid to local…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…
The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous…
Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…
Given a stochastic structure with a filtration $\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\mathbb{F}$ adapted non decreasing processes is considered. The…
Sociotechnological and geospatial processes exhibit time varying structure that make insight discovery challenging. To detect abnormal moments in these processes, a definition of `normal' must be established. This paper proposes a new…
Continuous-time random walks (CTRW) play important role in understanding of a wide range of phenomena. However, most theoretical studies of these models concentrate only on stationary-state dynamics. We present a new theoretical approach,…
Piecewise-deterministic Markov processes (PDMPs) offer a powerful stochastic modeling framework that combines deterministic trajectories with random perturbations at random times. Estimating their local characteristics (particularly the…
We consider a Markov jump process on a general state space to which we apply a time-dependent weak perturbation over a finite time interval. By martingale-based stochastic calculus, under a suitable exponential moment bound for the…
We investigate the concept of an asymptotic e-process, which is a doubly-indexed stochastic process $(E_{m,n})_{m,n\in\mathbb{N}}$ that possesses, asymptotically for an approximation index $m\to\infty$, the properties of an e-process along…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
This paper deals with inference in a class of stable but nearly-unstable processes. Autoregressive processes are considered, in which the bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with…
We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike…
Recent studies concerning the point electricity price forecasting have shown evidence that the hourly German Intraday Continuous Market is weak-form efficient. Therefore, we take a novel, advanced approach to the problem. A probabilistic…
A new model for time series with a specific oscillation pattern is proposed. The model consists of a hidden phase process controlling the speed of polling and a nonparametric curve characterizing the pattern, leading together to a…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…