9 papers
MA(1) processes with Laplace innovations conditioned to stay positive
Frank Aurzada, Virginia Worf
We study a moving-average process with (not necessarily symmetric) Laplace innovations under the constraint of positivity. In the three nondegenerate parameter regimes , $θ>…
Persistence probabilities of fractional Lévy fields indexed by hyperbolic space and other Riemannian manifolds
Frank Aurzada, Max Helmer
We study the persistence probability of fractional Lévy fields, i.e. the analogue of fractional Brownian motion with generalised (multi-dimensional) index sets. First, we compute t…
MA(1) processes with uniform innovations conditioned to stay positive in the non-expanding regime
Frank Aurzada, Virginia Worf
We study an MA(1)-process with uniform innovations conditioned to stay positive. Representing the model as a Markov chain, we prove the existence of the limiting finite-dimensional…
Persistence Probability of Fractional Brownian Motion with Random Hurst Exponent
Frank Aurzada, Sabine Müller
We study the persistence properties of a fractional Brownian motion whose Hurst exponent is a random variable instead of a fixed constant. For each fixed , it is well…
Persistence probabilities of MA(1) sequences with Laplace innovations and -deformed zigzag numbers
Frank Aurzada, Kilian Raschel
We study the persistence probabilities of a moving average process of order one with innovations that follow a Laplace distribution. The persistence probabilities can be computed f…
Persistence probabilities for MA(1) sequences with uniform innovations
Frank Aurzada, Kilian Raschel
We study the persistence probabilities of a moving average process of order one with uniform innovations. We identify a number of regions-characterized by the location of the unifo…
Persistence probabilities of spherical fractional Brownian motion
Frank Aurzada, Max Helmer
We compute the rate of decay of the persistence probabilities of spherical fractional Brownian motion, which was defined by Lévy (1965) and Istas (2005). The rate resembles the Euc…
The Best Time for an Update: Risk-Sensitive Minimization of Age-Based Metrics
Wanja de Sombre, Andrea Ortiz, Frank Aurzada +1
Popular methods to quantify transmitted data quality are the Age of Information (AoI), the Query Age of Information (QAoI), and the Age of Incorrect Information (AoII). We consider…
Persistence probabilities of a smooth self-similar anomalous diffusion process
Frank Aurzada, Pascal Mittenbühler
We consider the persistence probability of a certain fractional Gaussian process that appears in the Mandelbrot-van Ness representation of fractional Brownian motion. This pr…