Related papers: Two-term large-time asymptotic expansion of the va…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
Classical conditions for asymptotic stability of periodic solutions bifurcating from a limit cycle rely on the derivative of the corresponding bifurcation function F at the bifurcation point t. We show that for analytic systems this result…
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…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
This paper considers the infinite horizon optimal control problem for nonlinear systems. Under the condition of nonlinear controllability of the system to any terminal set containing the origin and forward invariance of the terminal set, we…
We develop a necessary stochastic maximum principle for a finite-dimensional stochastic control problem in infinite horizon under a polynomial growth and joint monotonicity assumption on the coefficients. The second assumption generalizes…
We consider the Navier--Stokes equations in a half-plane with a drift term parallel to the boundary and a small source term of compact support. We provide detailed information on the behavior of the velocity and the vorticity at infinity in…
We study the asymptotic behavior and the asymptotic stability of the two-dimensional Euler equations and of the two-dimensional linearized Euler equations close to parallel flows. We focus on spectrally stable jet profiles $U(y)$ with…
We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schr\"odinger equation by means of the Deift-Zhou nonlinear steepest descent method. The leading term is a sum of two terms that oscillate with decay…
The paper addresses an existence problem for infinite horizon optimal control when the system under control is exponentially stabilizable or stable. Classes of nonlinear control systems for which infinite horizon optimal controls exist are…
A theorem is proved on the uniform estimation of the residual term of the asymptotic expansion with respect to a small parameter of the solution of the initial problem for a singularly perturbed differential operator weakly nonlinear…
This paper is concerned with optimal control problems for a linear homogeneous stochastic differential equation having regime switching with purely quadratic functional in the large time horizons. We establish the so-called turnpike…
In this paper we extend our recent work on two-dimensional (2D) diffusive search-and-capture processes with multiple small targets (narrow capture problems) by considering an asymptotic expansion of the Laplace transformed probability flux…
We consider an optimal control problem with tracking-type cost functional constrained by the Cattaneo equation, which is a well-known model for delayed heat transfer. In particular, we are interested the asymptotic behaviour of the optimal…
We consider stochastic impulse control problems where the process is driven by a general one-dimensional diffusion. We shall show a new mathematical characterization of the value function as a linear function in a certain transformed space.…
A finite-horizon optimal estimation problem for discrete-time linear systems is formulated and solved. The formulation is a natural extension of that which yields a deadbeat observer. The resultant observer is the dual of the controller…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
We introduce $p$-uniformity to characterize the scaling of density fluctuations in spatial random systems in $\mathbb{R}^d$, ranging from hyperfluctuation to stealthy hyperuniformity. Our central theorem establishes sufficient conditions to…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
We derive a nonparametric higher-order asymptotic expansion for small-time changes of conditional characteristic functions of It\^o semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of…