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Difference-in-differences (DiD) identification relies mainly on a parallel trends assumption about untreated potential outcomes. Researchers often relax this assumption by assuming conditional parallel trends within units with the same…
Continuous Time Random Walks (CTRWs) are jump processes with random waiting times between jumps. We study scaling limits for CTRWs where the distribution of jumps and waiting times is coupled and varies in space and time. Such processes…
We analyze a modification of the Richards growth model by introducing a time-dependent perturbation in the growth rate. This modification becomes effective at a special switching time, which represents the first-crossing-time of the…
We evaluate the significance of a recently proposed bivariate jump-diffusion model for a data-driven characterization of interactions between complex dynamical systems. For various coupled and non-coupled jump-diffusion processes, we find…
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…
In this paper, we propose a novel stochastic process that serves as a natural discrete-time counterpart to the continuous-time model known as the ``Poisson hyperbolic staircase'' proposed by Levikson et al. (1999), and clarify its…
We derive a nonparametric higher-order asymptotic expansion for small-time changes of conditional characteristic functions of It\^o semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of…
This paper studies performance preserving event design in nonlinear event-based control systems based on a local L2-type performance criterion. Considering a finite gain local L2-stable disturbance driven continuous-time system, we propose…
Univariate isotonic regression (IR) has been used for nonparametric estimation in dose-response and dose-finding studies. One undesirable property of IR is the prevalence of piecewise-constant stretches in its estimates, whereas the…
We consider causal inference in dynamic settings where treatment is assigned by thresholding a state variable that can change over time. There is a large literature on regression-discontinuity methods building on the fact that, in the…
In this article the almost semi-continuous step-process $\xi (t)$ is considered. The conditional characteristic functions of the jumps of $\xi (t)$ have the form $\mathrm{E} [ e^{i\alpha \xi_k}/\xi_k>0 ]=c(c-i\alpha)^{-1}$. For such…
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…
We study a model of an infinite system of point particles in $\mathds{R}^d$ performing random jumps with attraction. The system's states are probability measures on the space of particle configurations, and their evolution is described by…
In this paper, we will consider a class of continuous-time stochastic control systems with both unknown nonlinear structure and unknown disturbances, and investigate the capability of the classical proportional-integral-derivative(PID)…
In this paper we introduce non-decreasing jump processes with independent and time non-homogeneous increments. Although they are not L\'evy processes, they somehow generalize subordinators in the sense that their Laplace exponents are…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main…
A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…