Related papers: Stochastic Functional Kolmogorov Equations (I): Pe…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
In this paper, a class of Kolmogorov systems with delays are studied. Sufficient conditions are provided for a system to have a compact uniform attractor. Then Jansen's result (J. Math. Biol. Vol. 25 (1987) 411-422) for autonomous…
Recently, a theoretical framework aimed at separating the roles of dynamics and topology in multi-dimensional systems has been developed (Gao et al, \textit{Nature}, Vol 530:307 (2016)). The validity of their method is assumed to hold…
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…
In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward…
A two-dimensional Kolmogorov system with two parameters and having a degenerate condition is studied in this work. We obtain local analytical properties of the system when the parameters vary in a sufficiently small neighborhood of the…
This paper starts from the Fisher-Kolmogorov-Petrovskii-Piskunov equation to model diffusive populations. The main result, according to this model, is that two connected patches in a system do not always contribute to each other.…
We propose an extension of the Plefka expansion, which is well known for the dynamics of discrete spins, to stochastic differential equations with continuous degrees of freedom and exhibiting generic nonlinearities. The scenario is…
We study a class of nonautonomous, linear, parabolic equations with unbounded coefficients on $\mathbb R^{d}$ which admit an evolution system of measures. It is shown that the solutions of these equations converge to constant functions as…
This paper is concerned with stochastic Hamiltonian systems which model a class of open dynamical systems subject to random external forces. Their dynamics are governed by Ito stochastic differential equations whose structure is specified…
We propose a novel approach for computing committor functions, which describe transitions of a stochastic process between metastable states. The committor function satisfies a backward Kolmogorov equation, and in typical high-dimensional…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
For the regime-switching diffusion process with and without advection term we propose an integro-differential equation describing the densities of states continuously distributed over a segment. We demonstrate that there exists a…
Given global Lipschitz continuity and differentiability of high enough order on the coefficients in It\^{o}'s equation, differentiability of associated semigroups, existence of twice differentiable solutions to Kolmogorov equations and weak…
We consider a Lotka-Volterra food chain model with possibly intra-specific competition in a stochastic environment represented by stochastic differential equations. In the non-degenerate setting, this model has already been studied by A.…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
In this paper, we study a new type of stochastic functional differential equations which is called hybrid pantograph stochastic functional differential equations. We investigate several moment properties and sample properties of the…