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The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…

In this paper we propose a new approach for sequential monitoring of a parameter of a $d$-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a…

Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…

A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…

Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive…

This paper provides robust, new evidence on the causal drivers of market troughs. We demonstrate that conclusions about these triggers are critically sensitive to model specification, moving beyond restrictive linear models with a flexible…

Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…

Event sequences can be modeled by temporal point processes (TPPs) to capture their asynchronous and probabilistic nature. We propose an intensity-free framework that directly models the point process distribution by utilizing normalizing…

We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…

We introduce a class of multifractal processes, referred to as Multifractal Random Walks (MRWs). To our knowledge, it is the first multifractal processes with continuous dilation invariance properties and stationary increments. MRWs are…

A temporal point process is a stochastic process that predicts which type of events is likely to happen and when the event will occur given a history of a sequence of events. There are various examples of occurrence dynamics in the daily…

At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…

In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the…

We study two-state (dichotomous, telegraph) random ergodic continuous-time processes with dynamics depending on their past. We take into account the history of process in an explicit form by introducing an integral non-local memory term…

We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…

We present a methodology for the study of the dispersion of trajectories of stochastic processes in reconstructed phase spaces from observed data. The methodology allows to find ensembles of analog states, i.e. states that are close in the…

These short lecture notes contain a not too technical introduction to point processes on the time line. The focus lies on defining these processes using the conditional intensity function. Furthermore, likelihood inference, methods of…

We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…

This paper introduces a novel periodogram-like function, called the expectile periodogram, for modeling spectral features of time series and detecting hidden periodicities. The expectile periodogram is constructed from trigonometric…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…