Related papers: Superdiffusive limits for deterministic fast-slow …

For a measure preserving dynamical system $(\mathcal{X},f, \mu)$, we consider the time series of maxima $M_n=\max\{X_1,\ldots,X_n\}$ associated to the process $X_n=\phi(f^{n-1}(x))$ generated by the dynamical system for some observable…

This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…

We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

We consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form \begin{align*} \partial_t \big( |u|^{q-1}u \big) - \operatorname{div} \big( D_\xi f(x,u,Du) \big) = - D_u f(x,u,Du) \end{align*} with $q \in (0, \infty)$ in a…

We consider solutions of L\'evy-driven stochastic differential equations of the form $\mathrm{d} X_t=\sigma(X_{t-})\mathrm{d} L_t$, $X_0=x$ where the function $\sigma$ is twice continuously differentiable and maximal of linear growth and…

Quantum speed limits such as the Mandelstam-Tamm or Margolus-Levitin bounds offer a quantitative formulation of the energy-time uncertainty principle that constrains dynamics over short times. We show that the spectral form factor, a…

The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…

We establish Liouville type theorems for elliptic systems with various classes of non-linearities on $\mathbb{R}^N$. We show among other things, that a system has no semi-stable solution in any dimension, whenever the infimum of the…

A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…

We consider a slow-fast stochastic differential system with L\'evy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated…

In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…

This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…

We introduce an explicit adaptive Milstein method for stochastic differential equations (SDEs) with no commutativity condition. The drift and diffusion are separately locally Lipschitz and together satisfy a monotone condition. This method…

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 treat the class of universal Markov processes on the d-dimensional Euklidean space which do not depend on random. For these, as well as for several subclasses, we prove criteria whether a function f, defined on the positive half-line,…

In this paper, we first analyze the strong and weak convergence of projective integration methods for multiscale stochastic dynamical systems driven by $\alpha$-stable processes, which are used to estimate the effect that the fast…

Symmetric matrix-valued dynamical systems are an important class of systems that can describe important processes such as covariance/second-order moment processes, or processes on manifolds and Lie Groups. We address here the case of…

We consider SDEs of the form $dX_t = |f(X_t)|/t^{\gamma} dt+1/t^{\gamma} dB_t$, where $f(x)$ behaves comparably to $|x|^k$ in a neighborhood of the origin, for $k\in [1,\infty)$. We show that there exists a threshold value…

This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…