Related papers: On Bellman's principle with inequality constraints

In this paper, under mild assumptions, we derive a law of large numbers, a central limit theorem with an error estimate, an almost sure invariance principle and a variant of Chernoff bound in finite-state hidden Markov models. These limit…

The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…

Motivated by applications in Markov chain Monte Carlo, we discuss what it means for one Markov chain to be an approximation to another. Specifically included in that discussion are situations in which a Markov chain with continuous state…

In the present paper, the maximum principle for finite horizon state constrained problems from the book by R. Vinter [\textit{Optimal Control}, Birkh\"auser, Boston, 2000; Theorem~9.3.1] is analyzed via parametric examples. The latter has…

In this paper we study a family of nonlinear (conditional) expectations that can be understood as a semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a time and path-dependent…

Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's…

In contrast to the wide-spread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where a separable quantum state does not satisfy the original Bell inequality although…

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch,…

D\"{u}r [Phys. Rev. Lett. {\bf 87}, 230402 (2001)] constructed $N$-qubit bound entangled states which violate a Bell inequality for $N\ge 8$, and his result was recently improved by showing that there exists an $N$-qubit bound entangled…

An approximation method for construction of optimal strategies in the bid \& ask limit order book in the high-frequency trading (HFT) is studied. The basis is the article by M. Avellaneda \& S. Stoikov 2008, in which certain seemingly…

We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…

We study violations of n particle Bell inequalities (as developed by Mermin and Klyshko) under the assumption that suitable partial transposes of the density operator are positive. If all transposes with respect to a partition of the system…

Many Bell test results violate Bell's inequality. The premise of Bell's inequality is local determinism. We propose that, it can't be proved that something's mechanism isn't deterministic; if loopholes are not the reason of violation of…

We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of…

We revisit the Markov approximation necessary to derive ordinary Brownian motion from a model widely adopted in literature for this specific purpose. We show that this leads to internal inconsistencies, thereby implying that further search…

For all Einstein-Podolsky-Rosen-type experiments on deterministic systems the Bell inequality holds, unless non-local interactions exist between certain parts of the setup. Here we show that in nonlinear systems the Bell inequality can be…

Bell's theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum…

This paper shows the usefulness of the Perov contraction theorem, which is a generalization of the classical Banach contraction theorem, for solving Markov dynamic programming problems. When the reward function is unbounded, combining an…

First, we present a Bell type inequality for n qubits, assuming that m out of the n qubits are independent. Quantum mechanics violates this inequality by a ratio that increases exponentially with m. Hence an experiment on n qubits violating…

This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.