Dynamic game arises as a powerful paradigm for multi-robot planning, which safety constraint satisfaction is crucial. Constrained stochastic games are of particular interest, real-world robots need to operate and satisfy constraints under uncertainty. Existing methods solving handle chance using exponential penalties with hand-tuned weights. However, finding suitable penalty weight nontrivial r...

The paper is concerned with two-person zero-sum mean-field linear-quadratic stochastic differential games over finite horizons. By a Hilbert space method, necessary condition and sufficient are derived for the existence of an open-loop saddle point. It shown that under condition, associated two Riccati equations admit unique strongly regular solutions, in terms which point can be represented as...

A common problem faced by statistical institutes is that data may be missing from collected datasets. The typical way to overcome this problem is to impute the missing data. The problem of imputing missing data is complicated by the fact that statistical data often have to satisfy certain edit rules and that values of variables across units sometimes have to sum up to known totals. For numerica...

Abstract. For any given integer q ≥ 2, we consider sets N of non-negative integers that are defined by linear relations between their q-adic digits (for example, the set of non-negative integers such that the number of 1’s equals twice the number of 0’s in the binary representation). The main goal is to prove that the sequence (αn)n∈N is uniformly distributed modulo 1 for all irrational numbers...