29 citations · 228 across the 47 of their papers we have counts for
57 papers
Ornstein-Uhlenbeck process conditioned to have restricted -norm
Frank Aurzada, Mikhail Lifshits, Max Wiegand
We condition an Ornstein-Uhlenbeck process on having an atypically small -norm on long time intervals. The weak limit of these conditioned processes is again an Ornstein-Uhlen…
Persistence exponents via perturbation theory: MA(1)-processes
Frank Aurzada, Dieter Bothe, Pierre-Étienne Druet +2
For the moving average process , , where and is an i.i.d. sequence of normally distributed random variables, we…
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…
Brownian motion conditioned to have restricted -norm
Frank Aurzada, Mikhail Lifshits, Dominic T. Schickentanz
We condition a Brownian motion on having an atypically small -norm on a long time interval. The obtained limiting process is a non-stationary Ornstein-Uhlenbeck process.
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 which is allowed to spend a total of time units outside a bounded interval does not leave the interval at all. This c…
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…