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We study a kind of better recurrence than Kolmogorov's one: periodicity recurrence,which corresponds periodic solutions in distribution for stochastic differential equations. On the basis of technique of upper and lower solutions and…
This work is concerned with the analysis of a stochastic approximation algorithm for the simulation of quasi-stationary distributions on finite state spaces. This is a generalization of a method introduced by Aldous, Flannery and Palacios.…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
The paper introduces a new numerical characteristic of one dimensional stochastic systems. This quantity is a measure of minimal periodicity, can be detected in the process deep differential structure. The claim is that this new measure of…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
We study absolutely periodic points and trajectories of Hamiltonian systems. Our main result is a necessary and sufficient for a Hamiltonian system to have the following property: if there exists one absolutely periodic trajectory then all…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions. It is shown…
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…
We study linear backward stochastic partial differential equations of parabolic type with special boundary conditions in time. The standard Cauchy condition at the terminal time is replaced by a condition that holds almost surely and mixes…
We consider an independently identically distributed random dynamical system generated by finitely many, non-uniformly expanding Markov interval maps with a finite number of branches. Assuming a topologically mixing condition and the…
In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
We consider the concept of statistical complexity to write the quasiperiodical damped systems applying the snapshot attractors. This allows us to understand the behaviour of these dynamical systems by the probability distribution of the…
In this paper, we study almost periodic solutions for semilinear stochastic differential equations driven by L\'{e}vy noise with exponential dichotomy property. Under suitable conditions on the coefficients, we obtain the existence and…
We show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact Abelian groups. This generalizes all earlier results of this type. Our…
For a general discrete dynamics on a Banach and Hilbert spaces we give a necessary and sufficient conditions of the existence of bounded solutions under assumption that the homogeneous difference equation admits an exponential dichotomy on…
In this paper we establish asymptotic (biasymptotic) equivalence between spaces of solutions of a given linear homogeneous system and a perturbed system. The perturbations are of either linear or weakly linear characters. Existence of a…
The notion of asymptotic unpredictability was recently introduced in (Commun. Nonlinear Sci. Numer. Simul. 134, 108029, 2024) for semiflows. Likewise unpredictable trajectories, asymptotically unpredictable ones are also capable of…