Related papers: Localisable moving average stable and multistable …
We prove a general result on a relationship between a limit of normalized numbers of interval crossings by a c\`adl\`ag path and an occupation measure associated with this path. Using this result we define local times of fractional Brownian…
Stochastic gradient descent is a classic algorithm that has gained great popularity especially in the last decades as the most common approach for training models in machine learning. While the algorithm has been well-studied when…
A bound uniform over various loss-classes is given for data generated by stationary and phi-mixing processes, where the mixing time (the time needed to obtain approximate independence) enters the sample complexity only in an additive way.…
Assuming that a L\'evy-Driven Ornstein-Uhlenbeck (or CAR(1)) processes is observed at discrete times $0$, $h$, $2h$,$\cdots$ $[T/h]h$. We introduce a step-by-step methodological approach on how a person would verify the model assumptions.…
Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we…
We consider the problem of static Bayesian inference for partially observed Levy-process models. We develop a methodology which allows one to infer static parameters and some states of the process, without a bias from the…
While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a…
We show that the moving arithmetic average is closely connected to a Gauss-Seidel type fixed point method studied by Bauschke, Wang and Wylie, and which was observed to converge only numerically. Our analysis establishes a rigorous proof of…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
Random walks and Lorentz processes serve as fundamental models for Brownian motion. The study of random walks is a favorite object of probability theory, whereas that of Lorentz processes belongs to the theory of hyperbolic dynamical…
Starting from a Huxley-type model for an agitated vibrational mode, we propose an embedding of standard active particle models in terms of two-temperature processes. One temperature refers to an ambient thermal bath, and the other…
The asymptotic behavior for fully coupled multiscale stochastic systems becomes much complicated when the fast processes do not locate in a compact space. An example is constructed to show that the averaged coefficients may become…
Ornstein-Uhlenbeck processes driven by general L\'{e}vy process are considered in this paper. We derive strongly consistent estimators for the moments of the underlying L\'{e}vy process and for the mean reverting parameter of the…
In this paper, we first prove that the local time associated with symmetric $\alpha$-stable processes is of bounded $p$-variation for any $p>\frac{2}{\alpha-1}$ partly based on Barlow's estimation of the modulus of the local time of such…
The stochastic dynamics of an active particle undergoing a constant speed and additionally driven by an overall fluctuating torque is investigated. The random torque forces are expressed by a stochastic differential equation for the angular…
Rare transitions in stochastic processes can often be rigorously described via an underlying large deviation principle. Recent breakthroughs in the classification of reversible stochastic processes as gradient flows have led to a connection…
Data-driven modelling and synthesis of motion is an active research area with applications that include animation, games, and social robotics. This paper introduces a new class of probabilistic, generative, and controllable motion-data…
First, we present some results about the H\"older continuity of the sample paths of so called dilatively stable processes which are certain infinitely divisible processes having a more general scaling property than self-similarity. As a…
We study the averaging of fronts moving with positive oscillatory normal velocity, which is periodic in space and stationary ergodic in time. The problem can be reformulated as the homogenization of coercive level set Hamilton-Jacobi…
Ornstein-Uhlenbeck process of bounded variation is introduced as a solution of an analogue of the Langevin equation with an integrated telegraph process replacing a Brownian motion. There is an interval $I$ such that the process starting…