Related papers: Stochastic differential equations on noncompact ma…
We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…
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…
We study the scattering rigidity problem for standard stationary manifolds using timelike geodesics with a fixed momentum. Taking advantage of the symmetry of this manifolds, we use Hamiltonian reduction to show that this problem is related…
This paper studies the second moment boundedness of solutions of linear stochastic delay differential equations. First, we give a framework, for general $\mathrm{N}$-dimensional linear stochastic differential equations with a single…
Living organisms maintain stable functioning amid environmental fluctuations through homeostasis, a property that preserves a system's behavior despite changes in environmental conditions. To elucidate homeostasis in stochastic biochemical…
We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to $\#^{g}(S^{n+1}\times S^{n})$, provided $n \geq 4$. This is an odd dimensional analogue of a recent homological stability result of S. Galatius and…
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential…
We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the Cauchy data are holomorphic on the complex…
The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found…
This paper studies the stochastic differential equation (SDE) associated to a two-level quantum system (qubit) subject to Hamiltonian evolution as well as unmonitored and monitored decoherence channels. The latter imply a stochastic…
We obtain some results of existence and continuity of physical measures through equilibrium states and apply these to non-uniformly expanding transformations on compact manifolds with non-flat critical sets, obtaining sufficient conditions…
A new explicit stochastic scheme of order 1 is proposed for solving commutative stochastic differential equations (SDEs) with non-globally Lipschitz continuous coefficients. The proposed method is a semi-tamed version of Milstein scheme to…
The existence of the unique strong solution for a class of stochastic differential equations with non-Lipschitz coefficients was established recently. In this paper, we shall investigate the dependence with respect to the initial values. We…
Based on the classical probability, the stability criteria for stochastic differential delay equations (SDDEs) where their coefficients are either linear or nonlinear but bounded by linear functions have been investigated intensively.…
We consider a class of nonlinear Fokker-Planck equations describing the dynamics of an infinite population of units within mean-field interaction. Relying on a slow-fast viewpoint and on the theory of approximately invariant manifolds we…
In this paper, we study geometric rigidity of Riemannian manifolds admitting stable solutions of certain elliptic problems (stability in a variational sense), that is, under suitable hypotheses, we are able to characterize the Riemannian…
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…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
We discuss some recent advances concerning the symmetry of stochastic differential equations, and in particular the interrelations between these and the integrability -- complete or partial -- of the equations.
The novelty of our paper is to establish results on asymptotic stability of mild solutions in $p$th moment to Riemann-Liouville fractional stochastic neutral differential equations (for short Riemann-Liouville FSNDEs) of order $\alpha \in…