Andreas Basse-O’Connor
YOU?
Author Swipe
View article: On the Regularity of Random 2-SAT and 3-SAT
On the Regularity of Random 2-SAT and 3-SAT Open
We consider the random $k$-SAT problem with $n$ variables, $m=m(n)$ clauses, and clause density $α=\lim_{n\to\infty}m/n$ for $k=2,3$. It is known that if $α$ is small enough, then the random $k$-SAT problem admits a solution with high prob…
View article: Quantative bounds for high-dimensional non-linear functionals of Gaussian processes
Quantative bounds for high-dimensional non-linear functionals of Gaussian processes Open
In this paper, we derive explicit quantitative Berry-Esseen bounds in the hyper-rectangle distance for high-dimensional, non-linear functionals of Gaussian processes, allowing for strong dependence between variables. Our main result shows …
View article: Exponential dimensional dependence in high-dimensional Hermite method of moments
Exponential dimensional dependence in high-dimensional Hermite method of moments Open
It is numerically well known that moment-based tests for Gaussianity and estimators become increasingly unreliable at higher moment orders; however, this phenomenon has lacked rigorous mathematical justification. In this work, we establish…
View article: Fourth-Moment Theorems for Sums of Multiple Integrals
Fourth-Moment Theorems for Sums of Multiple Integrals Open
Nualart & Pecatti ([Nualart and Peccati, 2005, Thm 1]) established the first fourth-moment theorem for random variables in a fixed Wiener chaos, i.e. they showed that convergence of the sequence of fourth moments to the fourth moment of th…
View article: Robust Design of Two-Level Non-Integer SMC Based on Deep Soft Actor-Critic for Synchronization of Chaotic Fractional Order Memristive Neural Networks
Robust Design of Two-Level Non-Integer SMC Based on Deep Soft Actor-Critic for Synchronization of Chaotic Fractional Order Memristive Neural Networks Open
In this study, a model-free PIφ-sliding mode control ( PIφ-SMC) methodology is proposed to synchronize a specific class of chaotic fractional-order memristive neural network systems (FOMNNSs) with delays and input saturation. The fractiona…
View article: Robust stabilization of fractional-order hybrid optical system using a single-input TS-fuzzy sliding mode control strategy with input nonlinearities
Robust stabilization of fractional-order hybrid optical system using a single-input TS-fuzzy sliding mode control strategy with input nonlinearities Open
Hybrid optical systems with integrated control mechanisms enable a dynamic adjustment of optical components, ensuring real-time optimization, adaptability to changing conditions, and precise functionality. This control requirement enhances…
View article: Some Results on Random Mixed SAT Problems
Some Results on Random Mixed SAT Problems Open
In this short paper we present a survey of some results concerning the random SAT problems. To elaborate, the Boolean Satisfiability (SAT) Problem refers to the problem of determining whether a given set of $m$ Boolean constraints over $n$…
View article: A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems
A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems Open
Over the past decade, fractional-order laser chaotic systems have attracted a lot of attention from a variety of fields, including theoretical research as well as practical applications, which has resulted in the development of a number of…
View article: Synchronization of Fractional-Order Delayed Neural Networks Using Dynamic-Free Adaptive Sliding Mode Control
Synchronization of Fractional-Order Delayed Neural Networks Using Dynamic-Free Adaptive Sliding Mode Control Open
In this work, a dynamic-free adaptive sliding mode control (adaptive-SMC) methodology for the synchronization of a specific class of chaotic delayed fractional-order neural network systems in the presence of input saturation is proposed. B…
View article: Asymptotic theory for quadratic variation of harmonizable fractional stable processes
Asymptotic theory for quadratic variation of harmonizable fractional stable processes Open
In this paper we study the asymptotic theory for quadratic variation of a harmonizable fractional $\al$-stable process. We show a law of large numbers with a non-ergodic limit and obtain weak convergence towards a Lévy-driven Rosenblatt ra…
View article: Local asymptotic self-similarity for heavy tailed harmonizable fractional Lévy motions
Local asymptotic self-similarity for heavy tailed harmonizable fractional Lévy motions Open
In this work we characterize the local asymptotic self-similarity of harmonizable fractional Lévy motions in the heavy tailed case. The corresponding tangent process is shown to be the harmonizable fractional stable motion. In addition, we…
View article: On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos
On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos Open
Infinite divisibility of a class of two-dimensional vectors with components in the second Wiener chaos is studied. Necessary and sufficient conditions for infinite divisibility are presented as well as more easily verifiable sufficient con…
View article: A Berry–Esseén theorem for partial sums of functionals of heavy-tailed moving averages
A Berry–Esseén theorem for partial sums of functionals of heavy-tailed moving averages Open
In this paper we obtain Berry–Esseén bounds on partial sums of functionals of heavy-tailed moving averages, including the linear fractional stable noise, stable fractional ARIMA processes and stable Ornstein–Uhlenbeck processes. Our rates …
View article: A Berry-Esseén theorem for partial sums of functionals of heavy-tailed moving averages
A Berry-Esseén theorem for partial sums of functionals of heavy-tailed moving averages Open
In this paper we obtain Berry-Esseén bounds on partial sums of functionals of heavy-tailed moving averages, including the linear fractional stable noise, stable fractional ARIMA processes and stable Ornstein-Uhlenbeck processes. Our rates …
View article: On limit theory for functionals of stationary increments Lévy driven moving averages
On limit theory for functionals of stationary increments Lévy driven moving averages Open
In this paper we present new limit theorems for variational functionals of stationary increments Lévy driven moving averages in the high frequency setting. More specifically, we will show the “law of large numbers” and a “central limit the…
View article: On limit theory for functionals of stationary increments Levy driven moving averages
On limit theory for functionals of stationary increments Levy driven moving averages Open
In this paper we obtain new limit theorems for variational functionals of high frequency observations of stationary increments Lévy driven moving averages. We will see that the asymptotic behaviour of such functionals heavily depends on th…
View article: On limit theory for Lévy semi-stationary processes
On limit theory for Lévy semi-stationary processes Open
In this paper, we present some limit theorems for power variation of Lévy semi-stationary processes in the setting of infill asymptotics. Lévy semi-stationary processes, which are a one-dimensional analogue of ambit fields, are moving aver…
View article: Local asymptotic self-similarity for heavy tailed harmonizable fractional Lévy motions
Local asymptotic self-similarity for heavy tailed harmonizable fractional Lévy motions Open
In this work we characterize the local asymptotic self-similarity of harmonizable fractional Lévy motions in the heavy tailed case. The corresponding tangent process is shown to be the harmonizable fractional stable motion. In addition, we…
View article: Local asymptotic self-similarity for heavy tailed harmonizable\n fractional L\\'evy motions
Local asymptotic self-similarity for heavy tailed harmonizable\n fractional L\\'evy motions Open
In this work we characterize the local asymptotic self-similarity of\nharmonizable fractional L\\'evy motions in the heavy tailed case. The\ncorresponding tangent process is shown to be the harmonizable fractional stable\nmotion. In additi…
View article: Multivariate stochastic delay differential equations and CAR representations of CARMA processes
Multivariate stochastic delay differential equations and CAR representations of CARMA processes Open
In this study we show how to represent a continuous time autoregressive moving average (CARMA) as a higher order stochastic delay differential equation, which may be thought of as a continuous-time equivalent of the AR($\infty$) representa…
View article: Power variation for a class of stationary increments Lévy driven moving averages
Power variation for a class of stationary increments Lévy driven moving averages Open
In this paper, we present some new limit theorems for power variation of $k$th order increments of stationary increments Lévy driven moving averages. In the infill asymptotic setting, where the sampling frequency converges to zero while th…
View article: On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos
On infinite divisibility of a class of two-dimensional vectors in the second Wiener chaos Open
Infinite divisibility of a class of two-dimensional vectors with components in the second Wiener chaos is studied. Necessary and sufficient conditions for infinite divisibility is presented as well as more easily verifiable sufficient cond…
View article: On infinite divisibility of a class of two-dimensional vectors in the\n second Wiener chaos
On infinite divisibility of a class of two-dimensional vectors in the\n second Wiener chaos Open
Infinite divisibility of a class of two-dimensional vectors with components\nin the second Wiener chaos is studied. Necessary and sufficient conditions for\ninfinite divisibility is presented as well as more easily verifiable sufficient\nc…
View article: Continuous-time models with an autoregressive structure
Continuous-time models with an autoregressive structure Open
In this paper we suggest two continuous-time models which exhibit an autoregressive structure. We obtain existence and uniqueness results and study the structure of the solution processes. One of the models, which corresponds to general st…
View article: Equivalent martingale measures for Lévy-driven moving averages and related processes
Equivalent martingale measures for Lévy-driven moving averages and related processes Open
In the present paper we obtain sufficient conditions for the existence of equivalent martingale measures for Lévy-driven moving averages and other non-Markovian jump processes. The conditions that we obtain are, under mild assumptions, als…
View article: A continuous-time framework for ARMA processes
A continuous-time framework for ARMA processes Open
Based on a vast literature on continuous-time moving average processes we suggest an analogue for an autoregressive structure, and from this we combine the two concepts to a model for stationary processes which exhibit an ARMA type behavio…
View article: On limit theory for Levy semi-stationary processes
On limit theory for Levy semi-stationary processes Open
In this paper we present some limit theorems for power variation of Lévy semi-stationary processes in the setting of infill asymptotics. Lévy semi-stationary processes, which are a one-dimensional analogue of ambit fields, are moving avera…
View article: Limit theorems for a class of stationary increments Levy driven moving averages
Limit theorems for a class of stationary increments Levy driven moving averages Open
In this paper we present some new limit theorems for power variation of $k$th order increments of stationary increments Lévy driven moving averages. In the infill asymptotic setting, where the sampling frequency converges to zero while the…