Related papers: Sublinear expectations for countable-state uncerta…

In this paper we investigate sublinear semigroups whose pointwise generators are given by non-local Hamilton-Jacobi-Bellman operators. Our main result provides a stochastic representation in terms of a family of sublinear (conditional)…

For any injective von Neumann algebra R and any discrete, countable group G, which acts by *-automorphisms on R, we construct an idempotent mapping of an ultra-weakly dense subspace of B(H) onto the reducerd crossed product von Neumann…

For a countable-state Markov decision process we introduce an embedding which produces a finite-state Markov decision process. The finite-state embedded process has the same optimal cost, and moreover, it has the same dynamics as the…

We consider the joint lower expectation of a finite-state imprecise stochastic process, defined using either the Ville-Vovk-Shafer natural extension or the Williams natural extension. In both cases, we show that it is continuous with…

In this paper we introduce a notion of tightness for a family of nonlinear expectations and show that the tightness can be applied to obtain weak compactness in a framework of nonlinear expectation space. This criterion is very useful for…

By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…

We give extensions of results on nonnegative matrix semigroups which deduce finiteness or boundedness of such semigroups from the corresponding local properties, e.g., from finiteness or boundedness of values of certain linear functionals…

Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for…

Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…

Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and non-defective processes and all possible scenarios we identify the corresponding…

We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing one. In particular, we may start with a superprocess,…

We study the Hsu-Robbins-Erd\"os theorem to the case when all moments under sub-linear expectations exist, but the moment generating function does not, viz, we suppose that…

Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…

We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely…

This paper proposes a new extended-state observer-based framework for adaptive nonlinear regulator design of a class of nonlinear systems, in the general nonequilibrium theory. By augmenting an extended-state observer with an internal…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…

Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized…

The sub-linear expectation space is a nonlinear expectation space having advantages of modelling the uncertainty of probability and distribution. In the sub-linear expectation space, we use capacity and sub-linear expectation to replace…

This paper tackles the problem of nonlinear systems, with sublinear growth but unbounded control, under perturbation of some time-varying state constraints. It is shown that, given a trajectory to be approximated, one can find a neighboring…