Zobrazeno 1 - 10
of 216
pro vyhledávání: '"Aurzada, Frank"'
For the moving average process $X_n=\rho \xi_{n-1}+\xi_n$, $n\in\mathbb{N}$, where $\rho\in\mathbb{R}$ and $(\xi_i)_{i\ge -1}$ is an i.i.d. sequence of normally distributed random variables, we study the persistence probabilities $\mathbb{P}(X_0\ge 0
Externí odkaz:
http://arxiv.org/abs/2407.06870
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 introduce a new simple combinatorial view on occupation times of stoc
Externí odkaz:
http://arxiv.org/abs/2406.09886
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 these metrics in a point-to-point wireless communication system, wher
Externí odkaz:
http://arxiv.org/abs/2401.10265
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.
Comment: 16 pages
Comment: 16 pages
Externí odkaz:
http://arxiv.org/abs/2312.12982
Autor:
Aurzada, Frank, Mittenbühler, Pascal
We consider the persistence probability of a certain fractional Gaussian process $M^H$ that appears in the Mandelbrot-van Ness representation of fractional Brownian motion. This process is self-similar and smooth. We show that the persistence exponen
Externí odkaz:
http://arxiv.org/abs/2311.03972
We show that a Brownian motion on $\mathbb{R}_{\ge 0}$ which is allowed to spend a total of $s > 0$ time units outside a bounded interval does not leave the interval at all. This can be seen as an extreme example of entropic repulsion. Moreover, we e
Externí odkaz:
http://arxiv.org/abs/2308.04866
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 the solution of the stochastic heat equation with zero boundary condi
Externí odkaz:
http://arxiv.org/abs/2305.03541
Publikováno v:
Nonlinear Analysis: Hybrid Systems, 53, 101494 (2024)
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 observation motivates numerous event-triggered control schemes, proving i
Externí odkaz:
http://arxiv.org/abs/2303.11097
It is well known that the employed triggering scheme has great impact on the control performance when control loops operate under scarce communication resources. Various practical and simulative works have demonstrated the potential of event-triggere
Externí odkaz:
http://arxiv.org/abs/2206.08862
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 minor conditions, we show that the asymptotic behaviour of the persis
Externí odkaz:
http://arxiv.org/abs/2201.08784