Motivated by entropy estimation from chaotic time series, we provide a comprehensive analysis of hitting times of cylinder sets in the setting of Gibbsian sources. We prove two strong approximation results from which we easily deduce pointwise convergence to entropy, lognormal fluctuations, precise large deviation estimates and an explicit formula for the hitting-time multifractal spectrum. It ...

In this paper we introduce a new method for the simulation of the exit time and exit position of a δ-dimensional Brownian motion from a domain. The main interest of our method is that it avoids splitting time schemes as well as inversion of complicated series. The method, called walk on moving spheres algorithm, was first introduced for hitting times of Bessel processes. In this study this meth...

A passive attacker can compromise a generic anonymity protocol by applying the so called disclosure attack, i.e. a special traffic analysis attack. In this work we present a more efficient way to accomplish this goal, i.e. we need less observations by looking for unique minimal hitting sets. We call this the hitting set attack or just HS-attack. In general, solving the minimal hitting set probl...

The problem of computing the moment generating function of the first passage time T to a > 0 or −b < 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T .

We study the tail behavior of the distribution of certain subadditive functionals acting on the sample paths of L evy processes. The functionals we consider have, roughly speaking, the following property: only the points of the process that lie above a certain curve contribute to the value of the functional. Our assumptions will make sure that the process ends up eventually below the curve. Our...

The hitting time, huv , of a random walk on a finite graph G, is the expected time for the walk to reach vertex v given that it started at vertex u. We present two methods of calculating the hitting time between vertices of finite graphs, along with applications to specific classes of graphs, including grids, trees, and the ’tadpole’ graphs. keywords: random walks, hitting time

We show that the hitting time of the discrete time quantum random walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum random walks. We provide the framework for quantum hitting time and give two alternative definitions to set the ground for its study on general graphs. We t...

We study the complexity of the Hitting Set problem in set systems (hypergraphs) that avoid certain sub-structures. In particular, we characterize the classical and parameterized complexity of the problem when the Vapnik-Chervonenkis dimension (VC-dimension) of the input is small. VC-dimension is a natural measure of complexity of set systems. Several tractable instances of Hitting Set with a ge...

We define encodings of a Process Hitting into a Petri Net and conversely. It results notably that • the Process Hitting is a sub-class of Petri Nets; • any safe Petri Net can be encoded into a weakly-bisimilar Process Hittings with 3 priority classes. We finally discuss the use of the encoding of a Petri Net into a Process Hitting for providing efficient static analysis of dynamical properties.