Related papers: On an example for the Uniform Tauberian theorem in…
The paper is concerned with two-person dynamic zero-sum games. We investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity, and the limit of value functions of…
In an optimal control framework, we consider the value $V_T(x)$ of the problem starting from state $x$ with finite horizon $T$, as well as the value $V_\lambda(x)$ of the $\lambda$-discounted problem starting from $x$. We prove that uniform…
For two-person dynamic zero-sum games (both discrete and continuous settings), we investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity and the limit of value…
We study the long-run properties of optimal control problems in continuous time, where the running cost of a control problem is evaluated by a probability measure over R_+. Li, Quincampoix and Renault [DCDS-A, 2016] introduced an asymptotic…
The paper is concerned with two-person games with saddle point. We investigate the limits of value functions for long-time-average payoff, discounted average payoff, and the payoff that follows a probability density. Most of our assumptions…
The paper is devoted to dynamic games. We consider a general enough framework, which is not limited to e.g. differential games and could accommodate both discrete and continuous time. Assuming common dynamics, we study two game families…
We provide general conditions ensuring that the value functions of some nonlinear stopping problems with finite horizon converge to the value functions of the corresponding problems with infinite horizon. Our result can be formulated as…
The long-time average behavior of the value function in the calculus of variations is known to be connected to the existence of the limit of the corresponding Abel means. Still in the Tonelli case, such a limit is in turn related to the…
We find a sharp combinatorial bound for the metric entropy of sets in R^n and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central…
A classical problem in ergodic continuous time control consists of studying the limit behavior of the optimal value of a discounted cost functional with infinite horizon as the discount factor $\lambda$ tends to zero. In the literature,…
This paper surveys Abelian and Tauberian theorems for long-range dependent random fields. We describe a framework for asymptotic behaviour of covariance functions or variances of averaged functionals of random fields at infinity and…
We prove in a dynamic programming framework that uniform convergence of the finite horizon values implies that asymptotically the average accumulated payoff is constant on optimal trajectories. We analyze and discuss several possible…
A Tauberian theorem deduces an asymptotic for the partial sums of a sequence of non-negative real numbers from analytic properties of an associated Dirichlet series. Tauberian theorems appear in a tremendous variety of applications, ranging…
In the paper [P. Cannarsa, C. Mendico, Asymptotic analysis for Hamilton-Jacobi- Bellman equations on Euclidean space, (2021) Arxiv], we proved the existence of the limit as the time horizon goes to infinity of the averaged value function of…
This paper continues the examination of inventory control in which the inventory is modelled by a diffusion process and a long-term average cost criterion is used to make decisions. The class of such models under consideration have general…
We study the asymptotic relations between certain singular and constrained control problems for one-dimensional diffusions with both discounted and ergodic objectives. By constrained control problems we mean that controlling is allowed only…
We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi variational inequalities. These equations are related to robust switching control problems introduced in [3]. We prove that, as time horizon…
We prove uniform convergence results for the integrated periodogram of a weakly dependent time series, namely a law of large numbers and a central limit theorem. These results are applied to Whittle's parametric estimation. Under general…
We consider optimal control problem with an integral cost which is a mean of a given function. As a particular case, the cost concerned is the Ces\`aro average. The limit of the value with Ces\`aro mean when the horizon tends to infinity is…
We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is that it provides quantitative convergence guarantees at a much…