Related papers: Long-Time Stability Analysis for Stochastic Evolut…
In this paper we propose and analyze finite element discontinuous Galerkin methods for the one- and two-dimensional stochastic Maxwell equations with multiplicative noise. The discrete energy law of the semi-discrete DG methods were…
This paper studies the long time stability of both stochastic heat equations on a bounded domain driven by a correlated noise and their approximations. It is popular for researchers to prove the intermittency of the solution which means…
A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…
We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability…
In the paper regularity of solutions to stochastic Volterra equations in a separable Hilbert space is studied. Sufficient conditions for the temporal and spatial regularity of stochastic convolutions corresponding to the equations under…
Many real-world systems exhibit ``noisy'' evolution in time; interpreting their finitely-sampled behavior as arising from continuous-time processes (in the It\^o or Stratonovich sense) has led to significant success in modeling and analysis…
In this paper, we characterize the topological support in Holder norm of the law of the solution to a stochastic wave equation with three-dimensional space variable is proved. This note is a continuation of [9] and [10]. The result is a…
We prove maximal $L^p$-regularity for the stochastic evolution equation \[\{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t), \qquad t\in [0,T], U(0) & = u_0, {aligned}.\] under the assumption that $A$ is a sectorial…
Learning stable dynamics from observed time-series data is an essential problem in robotics, physical modeling, and systems biology. Many of these dynamics are represented as an inputs-output system to communicate with the external…
This paper study the hyperexponential stabilization for infinite-dimensional system on Hilbert space by a distributed time depending control law. The well-posedness of the closed loop for every time is obtained through the use of maximal…
A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the…
A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium…
Kruse and Wu [Math. Comp. 88 (2019) 2793--2825] proposed a fully discrete randomized Galerkin finite element method for semilinear stochastic evolution equations (SEEs) driven by additive noise and showed that this method attains a temporal…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
In this paper, we consider stationarity of a class of second-order stochastic evolution equations with memory, driven by Wiener processes or Levy jump processes, in Hilbert spaces. The strategy is to formulate by reduction some first-order…
In this paper, we investigate the stochastic evolution equations (SEEs) driven by $\log$-Whittle-Mat$\acute{{\mathrm{e}}}$rn (W-M) random diffusion coefficient field and $Q$-Wiener multiplicative force noise. First, the well-posedness of…
We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly…
We examine the existence and uniqueness of invariant measures of a class of stochastic partial differential equations with Gaussian and Poissonian noise and its exponential convergence. This class especially includes a case of stochastic…