Related papers: Asymptotic behavior for delayed backward stochasti…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an…
In this paper, we establish the existence of large solutions of Hessian equations and obtain a new boundary asymptotic behavior of solutions.
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
In this work a discontinuous boundary-value problem with retarded argument which contains spectral parameter in the transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues…
This paper is concerned with a linear quadratic optimal control problem of delayed backward stochastic differential equations. An explicit representation is derived for the optimal control, which is a linear feedback of the entire past…
We consider delay differential equations with a polynomially distributed delay. We derive an equivalent system of delay differential equations, which includes just two discrete delays. The stability of the equivalent system and its…
We propose a new notion of Partial Inertial Manifold to study the long-time asymptotic behavior of dissipative differential equations. As shown on an example, such manifolds may exist in the cases when the classical Inertial manifold does…
We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint…
This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential equations in which the solutions of the unperturbed…
We consider a class of stochastic control problems with a delayed control, both in drift and diffusion, of the type dX t = $\alpha$ t--d (bdt + $\sigma$dW t). We provide a new characterization of the solution in terms of a set of Riccati…
In this paper, we study a delayed forward-backward stochastic control system in which all the coefficients depend on the state and control terms, and the control domain is not necessarily convex. A global stochastic maximum principle is…
It is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear abstract functional differential equations in both, the finite and infinite delay case. A generalization of the integral…
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…
The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.
This paper discusses a new type of anticipated backward stochastic differential equation with a time-delayed generator (DABSDEs, for short) driven by fractional Brownian motion, also known as fractional BSDEs, with Hurst parameter…
We study the long time behavior of the solution of a stochastic PDEs with random coefficients assuming that randomness arises in a different independent scale. We apply the obtained results to 2D- Navier--Stokes equations.