6 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…
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.
Persistence exponents via perturbation theory: MA(1)-processes
Frank Aurzada, Dieter Bothe, Pierre-Ãtienne Druet +2
For the moving average process , , where and is an i.i.d. sequence of normally distributed random variable…
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 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…
Time- versus event-triggered consensus of a single-integrator multi-agent system
David Meister, Frank Aurzada, Mikhail A. Lifshits +1
Event-triggered control has shown the potential for providing improved control performance at the same average sampling rate when compared to time-triggered control. While this obs…