Related papers: The suprema of infinitely divisible processes

Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…

It is shown that the boldface maximality principle for subcomplete forcing, together with the assumption that the universe has only set-many grounds, implies the existence of a (parameter-free) definable well-ordering of…

We introduce an infinitary first order linear logic with least and greatest fixed points. To ensure cut elimination, we impose a validity condition on infinite derivations. Our calculus is designed to reason about rich signatures of…

We study the supremum of some random Dirichlet polynomials with independent coefficients and obtain sharp upper and lower bounds for supremum expectation thus extending the results from our previous work (see…

Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…

We study the density of the supremum of a strictly stable L\'evy process. We prove that for almost all values of the index $\alpha$ -- except for a dense set of Lebesgue measure zero -- the asymptotic series which were obtained in A.…

We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…

Landauer's erasure principle is generalized to nondeterministic processes on systems having an arbitrary number of non-symmetrical logical states. The condition that the process is applied in the same way, irrespective of the initial…

We study in this paper the infinite-dimensional orthogonal Lie algebra $\mathcal{O}_C$ which consists of all bounded linear operators $T$ on a separable, infinite-dimensional, complex Hilbert space $\mathcal{H}$ satisfying $CTC=-T^*$, where…

Universal two-particle entanglement processes are analyzed in arbitrary dimensional Hilbert spaces. On the basis of this analysis the class of possible optimal universal entanglement processes is determined whose resulting output states do…

Let $\mathcal{S}$ be a commutative semigroup, and let $T$ be a sequence of terms from the semigroup $\mathcal{S}$. We call $T$ an (additively) {\sl irreducible} sequence provided that no sum of its some terms vanishes. Given any element $a$…

The diffusivity $D(t)$ of finite-range asymmetric exclusion processes on $\mathbb Z$ with non-zero drift is expected to be of order $t^{1/3}$. Sepp\"{a}l\"ainen and Bal\'azs recently proved this conjecture for the nearest neighbor case. We…

We characterize all possible independent symmetric alpha-stable (SaS) components of an SaS process, 0<alpha<2. In particular, we focus on stationary SaS processes and their independent stationary SaS components. We also develop a parallel…

We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…

We prove the dynamic programming principle for a class of diffusion processes controlled up to the time of exit from a cylindrical region $[0,T)\times G$. It is assumed that the functional to be maximized is in the Lagrange form with…

In this paper, we obtain a new estimate for uniform integrability under sublinear expectations. Based on this, we establish the limit theorems under nonlinear expectations dominated by sublinear expectations through tightness, and the limit…

We introduce new techniques allowing one to construct diagonals of bounded Hilbert space operators and operator tuples under "Blaschke-type" assumptions. This provides a new framework for a number of results in the literature and…

Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but…

This paper considers the computational hardness of computing expected outcomes and deciding almost-sure termination of probabilistic programs. We show that deciding almost-sure termination and deciding whether the expected outcome of a…

We show that a restricted version of a conjecture of M. Talagrand on the relation between "expectation thresholds" and "fractional expectation thresholds" follows easily from a strong version of a second conjecture of Talagrand, on…