Related papers: Sublinear expectations for countable-state uncerta…
Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…
In this study, we propose the sublinear expectation structure under countable state space. To describe an interesting "nonlinear randomized" trial, based on a convex compact domain, we introduce a family of probability measures under…
An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations…
We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a…
We present a probabilistic construction of $\mathbb{R}^d$-valued non-linear affine processes with jumps. Given a set $\Theta$ of affine parameters, we define a family of sublinear expectations on the Skorokhod space under which the…
We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden…
In this book, we introduce a new approach of sublinear expectation to deal with the problem of probability and distribution model uncertainty. We a new type of (robust) normal distributions and the related central limit theorem under…
We provide extension procedures for nonlinear expectations to the space of all bounded measurable functions. We first discuss a maximal extension for convex expectations which have a representation in terms of finitely additive measures.…
We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued…
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…
In this paper we consider a sequence of random variables with mean uncertainty in a sublinear expectation space. Without the hypothesis of identical distributions, we show a new central limit theorem under the sublinear expectations.
We consider the problem of filtering an unseen Markov chain from noisy observations, in the presence of uncertainty regarding the parameters of the processes involved. Using the theory of nonlinear expectations, we describe the uncertainty…
This paper studies the propagation of finite-sample uncertainty under nonlinear transformations commonly used in statistical decision systems. In particular, we consider process capability indices, which are widely used in manufacturing…
This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…
We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of…
Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice (integer submodular functions) has recently attracted much interest,…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a stochastic process with uncertain parameters. We develop a general framework which can be seen as a version of the martingale problem method…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…