In this note, we present the necessary mathematical framework for stochastic MPEC models, including some new results on the existence of solutions and on convexity and diierentiability of the implicit upper-level objective function. In so doing, we clarify the links between these models and two-stage stochastic programs with recourse.

where F = {yh(x) : ∀ h ∈ H} and φ(h(x), y) is the loss function of interest. The labeled training sample S = {(xi, yi) | i ∈ {1, ..., n}, xi ∈ R, yi ∈ {±1}} is assumed to be generated from an independent, identically distributed (IID) random process. Given each Rademacher random variable σi ∈ {±1} with uniform odds, a realization of the Rademacher random variables σ amounts to a partition of th...

We study Nash equilibrium in two-settlement competitive electricity markets with horizontal market power, flow congestion, demand uncertainties and probabilistic system contingencies. The equilibrium is formulated as a stochastic Equilibrium Problem with Equilibrium Constraints (EPEC) in which each firm solves a stochastic Mathematical Program with Equilibrium Constraints (MPEC). We assume a no...

A natural non-Markovian extension of the theory of white noise quantum trajectories is presented. In order to introduce memory effects in the formalism an Ornstein-Uhlenbeck coloured noise is considered as the output driving process. Under certain conditions a random Hamiltonian evolution is recovered. Moreover, non-Markovian stochastic Schrödinger equations which unravel non-Markovian master e...

Theories can be produced by individuals seeking a good reputation of knowledge. Hence, a significant question is how to test theories anticipating that they might have been produced by (potentially uninformed) experts who prefer their theories not to be rejected. If a theory that predicts exactly like the data generating process is not rejected with high probability then the test is said to not...

The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. We begin with a complete graph on n vertices and proceed to remove the edges of triangles one at a time, where each triangle removed is chosen uniformly at random from the collection of all remaining triangles. This stochastic process terminates once it arrives at a triangle-free graph. In ...

We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete-time random process. As a result, we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully...

This condition is equivalent to stochastic mixability as well as the pseudoprobability convexity (PPC) condition, both defined by Van Erven et al. (2015). To be precise, for stochastic mixability, in Definition 4.1 of Van Erven et al. (2015), take their Fd and F both equal to our F , their P equal to {P}, and ψ(f) = f∗; then strong stochastic mixability holds. Likewise, for the PPC condition, i...