Related papers: Asymptotic behavior for delayed backward stochasti…
The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and…
In this paper, we study a large deviation principle for the solution of a backward stochastic differential equation driven by $G$-Brownian motion with subdifferential operator.
In this paper, we investigate the well-posedness and asymptotic behavior of difference equations of the form $x(t) = A x(t - \tau(t))$, $t \geq 0$, where the unknown function $x$ takes values in $\mathbb R^d$ for some positive integer $d$,…
We prove a stochastic maximum principle for a control problem where the state equation is delayed both in the state and in the control, and also the final cost functional may depend on the past trajectories. The adjoint equations turn out…
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…
In this paper we prove some uniqueness results for quadratic backward stochastic differential equations without any convexity assumptions on the generator. The bounded case is revisited while some new results are obtained in the unbounded…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
In this paper, we provide an estimate for the solutions of reflected backward stochastic differential equations (RBSDEs) driven by a Markov chain, derive a continuous dependence property for their solutions with respect to the parameters of…
Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…
In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…
We obtain a large deviation principle describing the small time asymptotics of the solution of a stochastic evolution equation with multiplicative noise. Our assumptions are a condition on the linear drift operator that is satisfied by…
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…
We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some examples, crude schemes fail to capture the correct limiting…
This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational…
We study the asymptotic behavior of a diffusion process with small diffusion in a domain $D$. This process is reflected at $\partial D$ with respect to a co-normal direction pointing inside $D$. Our asymptotic result is used to study the…
The goal of the present paper is to present a new approach to the construction of asymptotic (approximating) solutions to parabolic PDE by using the characteristics.
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…
We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded in terms of solutions of…
In this paper, we investigate a general class of stochastic gradient descent (SGD) algorithms, called Conditioned SGD, based on a preconditioning of the gradient direction. Using a discrete-time approach with martingale tools, we establish…