Related papers: On convergence of solutions to difference equation…

The perturbation theory of operator semigroups is used to derive response formulas for a variety of combinations of acting forcings and reference background dynamics. In the case of background stochastic dynamics, we decompose the response…

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied…

Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…

In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…

We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally…

We analyze the robustness of optimally controlled evolution equations with respect to spatially localized perturbations. We prove that if the involved operators are domain-uniformly stabilizable and detectable, then these localized…

The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique…

In stochastic multistable systems driven by the gradient of a potential, transitions between equilibria is possible because of noise. We study the ability of linear delay feedback control to mitigate these transitions, ensuring that the…

In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well…

Motivated by studies of indirect measurements in quantum mechanics, we investigate stochastic differential equations with a fixed point subject to an additional infinitesimal repulsive perturbation. We conjecture, and prove for an important…

We consider a non-homogeneous nonlinear stochastic difference equation X_{n+1} = X_n (1 + f(X_n)\xi_{n+1}) + S_n, and its important special case X_{n+1} = X_n (1 + \xi_{n+1}) + S_n, both with initial value X_0, non-random decaying free…

We study the long-time behaviour of solutions to a class of $d$-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H \in (0,1)$. The drift consists of a dissipative Lipschitz term and a…

The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…

We consider the long-time behavior of systems close to a system with a smooth first integral. Under certain assumptions, the limiting behavior, to some extent, turns out to be universal: it is determined by the first integral, the…

In this paper, we study an ordinary differential equation with a degenerate global attractor at the origin, to which we add a white noise with a small parameter that regulates its intensity. Under general conditions, for any fixed…

We consider primal-dual pairs of semidefinite programs and assume that they are ill-posed, i.e., both primal and dual are either weakly feasible or weakly infeasible. Under such circumstances, strong duality may break down and the primal…

We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…

We consider parabolic stochastic partial differential equations driven by white noise in time. We prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions. These conditions…

In this article we study a small random perturbation of a linear recurrence equation. If all the roots of its corresponding characteristic equation have modulus strictly less than one, the random linear recurrence goes exponentially fast to…

A prototype model of a stochastic one-variable system with a linear restoring force driven by two cross-correlated multiplicative and additive Gaussian white noises was considered earlier [S. I. Denisov et al., Phys. Rev. E 68, 046132…