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Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard…
Non-Markovian models have great expressive power, at the cost of complex analysis of the stochastic process. The method of Stochastic State Classes (SSCs) derives closed-form analytical expressions for the joint Probability Density…
Single-molecule experiments provide insight into the motion (conformational dynamics) of individual protein molecules. Usually, a well-defined but coarse-grained intramolecular coordinate is measured and subsequently analysed with the help…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
We analyze the effect of additive fractional noise with Hurst parameter $H > \frac{1}{2}$ on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet,…
We examine two stochastic processes with random parameters, which in their basic versions (i.e., when the parameters are fixed) are Gaussian and display long range dependence and anomalous diffusion behavior, characterized by the Hurst…
Stochastic thermodynamics investigates energetic and entropic bounds in small systems. Foundational results, e.g., the first and second laws, predominantly rely on the Markov (memoryless) assumption. Although physicists recognise that the…
The dynamics of a wide range of real systems, from email patterns to earthquakes, display a bursty, intermittent nature, characterized by short timeframes of intensive activity followed by long times of no or reduced activity. The…
The effect of short-term and long-term memory on spontaneous aggregation of organisms is investigated using a stochastic agent-based model. Each individual modulates the amplitude of its random motion according to the perceived local…
Inference in hidden Markov model has been challenging in terms of scalability due to dependencies in the observation data. In this paper, we utilize the inherent memory decay in hidden Markov models, such that the forward and backward…
Motivated by multiple applications in social networks, nervous systems, and financial risk analysis, we consider the problem of learning the underlying (directed) influence graph or causal graph of a high-dimensional multivariate…
A discrete-time random process is described which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time $t$ is given by a fixed probability $x$, is modified to include a memory…
Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is…
Inhomogeneous temporal processes in natural and social phenomena have been described by bursts that are rapidly occurring events within short time periods alternating with long periods of low activity. In addition to the analysis of…
A reasonable description of the degradation process is essential for credible reliability assessment in accelerated degradation testing. Existing methods usually use Markovian stochastic processes to describe the degradation process.…
The scaled Brownian motion (SBM) is regarded as one of the paradigmatic random processes, featuring the anomalous diffusion property characterized by the diffusion exponent. It is a Gaussian, self-similar process with independent…
Process mining is a well-established discipline of data analysis focused on the discovery of process models from information systems' event logs. Recently, an emerging subarea of process mining, known as stochastic process discovery, has…
We consider the effects of memory on the stationary behavior of a two-dimensional Langevin dynamics in a confining potential. The system is treated in an overdamped approximation and the degrees of freedom are under the influence of…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
This article develops nonparametric cointegrating regression models with endogeneity and semi-long memory. We assume that semi-long memory is produced in the regressor process by tempering of random shock coefficients. The fundamental…