F. Aurzada

activity

20072026

most citedPersistence probabilities \& exponents

29 citations · 228 across the 47 of their papers we have counts for

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51 papers · 1 filter

math.PR2026

Ornstein-Uhlenbeck process conditioned to have restricted $L_{2}$ -norm

Frank Aurzada, Mikhail Lifshits, Max Wiegand

We condition an Ornstein-Uhlenbeck process on having an atypically small $L_{2}$ -norm on long time intervals. The weak limit of these conditioned processes is again an Ornstein-Uhlen…

math.PR2024

Persistence exponents via perturbation theory: MA(1)-processes

Frank Aurzada, Dieter Bothe, Pierre-Étienne Druet +2

For the moving average process $X_{n} = ρ ξ_{n - 1} + ξ_{n}$ , $n \in N$ , where $ρ \in R$ and $(ξ_{i})_{i \geq - 1}$ is an i.i.d. sequence of normally distributed random variables, we…

math.PR2024

Occupation times and areas derived from random sampling

Frank Aurzada, Leif Döring, Helmut H. Pitters

We consider the occupation area of spherical (fractional) Brownian motion, i.e. the area where the process is positive, and show that it is uniformly distributed. For the proof, we…

math.PR2023

Brownian motion conditioned to have restricted $L_{2}$ -norm

Frank Aurzada, Mikhail Lifshits, Dominic T. Schickentanz

We condition a Brownian motion on having an atypically small $L_{2}$ -norm on a long time interval. The obtained limiting process is a non-stationary Ornstein-Uhlenbeck process.

math.PR2023

Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion

Frank Aurzada, Martin Kolb, Dominic T. Schickentanz

We show that a Brownian motion on $R_{\geq 0}$ which is allowed to spend a total of $s > 0$ time units outside a bounded interval does not leave the interval at all. This c…

math.PR2023

Scaling limit of stretched Brownian chains

Frank Aurzada, Volker Betz, Mikhail Lifshits

We show that a properly scaled stretched long Brownian chain converges to a two-parametric stochastic process, given by the sum of an explicit deterministic continuous function and…

math.PR2022

Persistence probabilities of mixed FBM and other mixed processes

Frank Aurzada, Martin Kilian, Ercan Sönmez

We consider the sum of two self-similar centred Gaussian processes with different self-similarity indices. Under non-negativity assumptions of covariance functions and some further…

math.PR2021★ 2 cited

Brownian Motion Conditioned to Spend Limited Time Below a Barrier

Frank Aurzada, Dominic T. Schickentanz

We condition a Brownian motion with arbitrary starting point $y \in R$ on spending at most $1$ time unit below $0$ and provide an explicit description of the resulting pro…

math.PR2020★ 1 cited

Universal break law for chains of Brownian particles with nearest neighbour interaction

Frank Aurzada, Volker Betz, Mikhail Lifshits

We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise potential $U$ , with one end of the chain fixed and the other end pulled away, i…

math.PR2020★ 6 cited

Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion

Frank Aurzada, Martin Kilian

We consider the persistence probability for the integrated fractional Brownian motion and the fractionally integrated Brownian motion with parameter $H,$ respectively. For the inte…

math.PR2020★ 3 cited

Persistence probabilities of weighted sums of stationary Gaussian sequences

Frank Aurzada, Sumit Mukherjee

With ${ξ_{i}}_{i \geq 0}$ being a centered stationary Gaussian sequence with non-negative correlation function $ρ (i) := E [ξ_{0} ξ_{i}]$ and ${σ (i)}_{i \geq 1}$ a sequence of posit…

math.PR2019

Breaking a chain of interacting Brownian particles

Frank Aurzada, Volker Betz, Mikhail Lifshits

We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise quadratic potential, with one end of the chain fixed and the other end pulled a…

math.PR2019★ 1 cited

Penalizing fractional Brownian motion for being negative

Frank Aurzada, Micha Buck, Martin Kilian

We study a modification of the fractional analogue of the Brownian meander, which is Brownian motion conditioned to be positive on the time interval $[0, 1]$ . More precisely, we d…

math.PR2019

Large deviations for infinite weighted sums of stretched exponential random variables

Frank Aurzada

We study the large deviation probabilities of infinite weighted sums of independent random variables that have stretched exponential tails. This generalizes Kiesel and Stadtmüller…

math.PR2019

Ruin probabilities in the Cramér-Lundberg model with temporarily negative capital

Frank Aurzada, Micha Buck

We study the asymptotics of the ruin probability in the Cramér-Lundberg model with a modified notion of ruin. The modification is as follows. If the portfolio becomes negative, the…

math.PR2018★ 3 cited

Persistence exponents via perturbation theory: AR(1)-processes

Frank Aurzada, Marvin Kettner

For AR(1)-processes $X_{n} = ρ X_{n - 1} + ξ_{n}$ , $n \in N$ , where $ρ \in R$ and $(ξ_{i})_{i \in N}$ is an i.i.d. sequence of random variables, we study the persistence pr…

math.PR2018

The first exit time of fractional Brownian motion from a parabolic domain

Frank Aurzada, Mikhail Lifshits

We study the first exit time of a multi-dimensional fractional Brownian motion from unbounded domains. In particular, we are interested in the upper tail of the corresponding distr…

math.PR2018

Scaling limits for a random boxes model

Frank Aurzada, Sebastian Schwinn

We consider random rectangles in $R^{2}$ that are distributed according to a Poisson random measure, i.e., independently and uniformly scattered in the plane. The distributi…

math.PR2018

How complex is a random picture?

Frank Aurzada, Mikhail Lifshits

We study the amount of information that is contained in "random pictures", by which we mean the sample sets of a Boolean model. To quantify the notion "amount of information", two…

math.PR2017★ 8 cited

Persistence probabilities of two-sided (integrated) sums of correlated stationary Gaussian sequences

Frank Aurzada, Micha Buck

We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brow…

math.PR2017

Persistence exponents in Markov chains

Frank Aurzada, Sumit Mukherjee, Ofer Zeitouni

We prove the existence of the persistence exponent $lo g λ := n \to \infty lim \frac{1}{n} lo g P_{μ} (X_{0} \in S, \dots, X_{n} \in S)$ for a class of time homogeneous Markov chains…

math.PR2016

Improving the performance of polling models using forced idle times

Frank Aurzada, Sebastian Schwinn

We consider polling models in the sense of Takagi (MIT Press, 1986). In our case, the feature of the server is that it may be forced to wait idly for new messages at an empty queue…

math.PR2016

Persistence probabilities and a decorrelation inequality for the Rosenblatt process and Hermite processes

Frank Aurzada, Christian Mönch

We study persistence probabilities of Hermite processes. As a tool, we derive a general decorrelation inequality for the Rosenblatt process, which is reminiscent of Slepian's lemma…

math.PR2016★ 5 cited

Random walks and branching processes in correlated Gaussian environment

Frank Aurzada, Alexis Devulder, Nadine Guillotin-Plantard +1

We study persistence probabilities for random walks in correlated Gaussian random environment first studied by Oshanin, Rosso and Schehr. From the persistence results, we can deduc…

Ornstein-Uhlenbeck process conditioned to have restricted L2​-norm

Persistence exponents via perturbation theory: MA(1)-processes

Occupation times and areas derived from random sampling

Brownian motion conditioned to have restricted L2​-norm

Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion

Scaling limit of stretched Brownian chains

Persistence probabilities of mixed FBM and other mixed processes

Brownian Motion Conditioned to Spend Limited Time Below a Barrier

Universal break law for chains of Brownian particles with nearest neighbour interaction

Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion

Persistence probabilities of weighted sums of stationary Gaussian sequences

Breaking a chain of interacting Brownian particles

Penalizing fractional Brownian motion for being negative

Large deviations for infinite weighted sums of stretched exponential random variables

Ruin probabilities in the Cramér-Lundberg model with temporarily negative capital

Persistence exponents via perturbation theory: AR(1)-processes

The first exit time of fractional Brownian motion from a parabolic domain

Scaling limits for a random boxes model

How complex is a random picture?

Persistence probabilities of two-sided (integrated) sums of correlated stationary Gaussian sequences

Persistence exponents in Markov chains

Improving the performance of polling models using forced idle times

Persistence probabilities and a decorrelation inequality for the Rosenblatt process and Hermite processes

Random walks and branching processes in correlated Gaussian environment

Ornstein-Uhlenbeck process conditioned to have restricted $L_{2}$ -norm

Brownian motion conditioned to have restricted $L_{2}$ -norm