相关论文: Stochastic difference equations with the Allee eff…

We revisit the problem of condensation for independent, identically distributed random variables with a power-law tail, conditioned by the value of their sum. For large values of the sum, and for a large number of summands, a condensation…

Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…

Nonlinear stochastic differential equations provide one of the mathematical models yielding 1/f noise. However, the drawback of a single equation as a source of 1/f noise is the necessity of power-law steady-state probability density of the…

We consider the joint lower expectation of a finite-state imprecise stochastic process, defined using either the Ville-Vovk-Shafer natural extension or the Williams natural extension. In both cases, we show that it is continuous with…

The global boundedness and asymptotic behavior are investigated for the solutions of a nonlocal time fractional reaction-diffusion equation (NTFRDE) $$ \frac{\partial^{\alpha }u}{\partial t^{\alpha }}=\Delta u+\mu u^{2}(1-kJ*u)-\gamma u,…

A Neumann problem in the strip for the Fitzhugh Nagumo system is consid- ered. The transformation in a non linear integral equation permits to deduce a priori estimates for the solution. A complete asymptotic analysis shows that for large t…

This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…

Phase transitions, sharp in the thermodynamic limit, get smeared in finite systems where macroscopic order-parameter fluctuations dominate. Achieving a coherent and complete theoretical description of these fluctuations is a central…

Let $X=(X_1,\ldots,X_n)$ be a vector of i.i.d. random variables where $X_i$'s take values over $\mathbb{N}$. The purpose of this paper is to study the number of weakly increasing subsequences of $X$ of a given length $k$, and the number of…

A general approach to a broad class of asymptotic problems related to long-time influence of small perturbations, of both deterministic and stochastic type, is presented in the paper. The main characteristic of this influence is a limiting…

The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimensional stochastic ordinary differential equations with…

An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain $D\subset\R^n$\,, $1\leq…

This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially H\"older continuous drifts and locally H\"older continuous diffusion coefficients. To handle with the superlinear terms in…

An effect generated by the nonexponential behavior of the survival amplitude of an unstable state at the long time region is considered. It is known that this amplitude tends to zero as $t$ goes to the infinity more slowly than any…

We consider the stochastic fractional heat equation $\partial_{t}u=\triangle^{\alpha/2}u+\lambda\sigma(u)\dot{w}$ on $[0,L]$ with Dirichlet boundary conditions, where $\dot{w}$ denotes the space-time white noise. For any $\lambda>0$, we…

Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…

The small and large size behavior of stationary solutions to the fragmentation equation with size diffusion is investigated. It is shown that these solutions behave like stretched exponentials for large sizes, the exponent in the…

Existence, uniqueness, and $L_p$-approximation results are presented for scalar stochastic differential equations (SDEs) by considering the case where, the drift coefficient has finitely many spatial discontinuities while both coefficients…

For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…

We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…