Stability analysis of fractional-order systems with randomly time-varying parameters

This paper is concerned with the stability of fractional-order systems with randomly timevarying parameters. Two approaches are provided to check the stability of such systems in mean sense. The first approach is based on suitable Lyapunov functionals to assess the stability, which is of vital importance in the theory of stability. By an example one finds that the stability conditions obtained by the first approach can be tabulated for some special cases. For some complicated linear and nonlinear systems, the stability conditions present computational difficulties. The second alternative approach is based on integral inequalities and ingenious mathematical method. Finally, we also give two examples to demonstrate the feasibility and advantage of the second approach. Compared with the stability conditions obtained by the first approach, the stability conditions obtained by the second one are easily verified by simple computation rather than complicated functional construction. The derived criteria improve the existing related results

Forecasting high waters at Venice Lagoon using chaotic time series analisys and nonlinear neural netwoks

Time series analysis using nonlinear dynamics systems theory and multilayer neural networks models have been applied to the time sequence of water level data recorded every hour at 'Punta della Salute' from Venice Lagoon during the years 1980-1994. The first method is based on the reconstruction of the state space attractor using time delay embedding vectors and on the characterisation of invariant properties which define its dynamics. The results suggest the existence of a low dimensional chaotic attractor with a Lyapunov dimension, DL, of around 6.6 and a predictability between 8 and 13 hours ahead. Furthermore, once the attractor has been reconstructed it is possible to make predictions by mapping local-neighbourhood to local-neighbourhood in the reconstructed phase space. To compare the prediction results with another nonlinear method, two nonlinear autoregressive models (NAR) based on multilayer feedforward neural networks have been developed. From the study, it can be observed that nonlinear forecasting produces adequate results for the 'normal' dynamic behaviour of the water level of Venice Lagoon, outperforming linear algorithms, however, both methods fail to forecast the 'high water' phenomenon more than 2-3 hours ahead.Publicad

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

A switching control for finite-time synchronization of memristor-based BAM neural networks with stochastic disturbances

This paper deals with the finite-time stochastic synchronization for a class of memristorbased bidirectional associative memory neural networks (MBAMNNs) with time-varying delays and stochastic disturbances. Firstly, based on the physical property of memristor and the circuit of MBAMNNs, a MBAMNNs model with more reasonable switching conditions is established. Then, based on the theory of Filippov’s solution, by using Lyapunov–Krasovskii functionals and stochastic analysis technique, a sufficient condition is given to ensure the finite-time stochastic synchronization of MBAMNNs with a certain controller. Next, by a further discussion, an errordependent switching controller is given to shorten the stochastic settling time. Finally, numerical simulations are carried out to illustrate the effectiveness of theoretical results

Large Deviations for Nonlocal Stochastic Neural Fields

We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a $Q$-Wiener process and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substanial difficulties but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multi-scale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations.Comment: 29 page

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed

Analysing behavioural factors that impact financial stock returns. The case of COVID-19 pandemic in the financial markets.

This thesis represents a pivotal advancement in the realm of behavioural finance, seamlessly integrating both classical and state-of-the-art models. It navigates the performance and applicability of the Irrational Fractional Brownian Motion (IFBM) model, while also delving into the propagation of investor sentiment, emphasizing the indispensable role of hands-on experiences in understanding, applying, and refining complex financial models. Financial markets, characterized by ’fat tails’ in price change distributions, often challenge traditional models such as the Geometric Brownian Motion (GBM). Addressing this, the research pivots towards the Irrational Fractional Brownian Motion Model (IFBM), a groundbreaking model initially proposed by (Dhesi and Ausloos, 2016) and further enriched in (Dhesi et al., 2019). This model, tailored to encapsulate the ’fat tail’ behaviour in asset returns, serves as the linchpin for the first chapter of this thesis. Under the insightful guidance of Gurjeet Dhesi, a co-author of the IFBM model, we delved into its intricacies and practical applications. The first chapter aspires to evaluate the IFBM’s performance in real-world scenarios, enhancing its methodological robustness. To achieve this, a tailored algorithm was crafted for its rigorous testing, alongside the application of a modified Chi-square test for stability assessment. Furthermore, the deployment of Shannon’s entropy, from an information theory perspective, offers a nuanced understanding of the model. The S&P500 data is wielded as an empirical testing bed, reflecting real-world financial market dynamics. Upon confirming the model’s robustness, the IFBM is then applied to FTSE data during the tumultuous COVID-19 phase. This period, marked by extraordinary market oscillations, serves as an ideal backdrop to assess the IFBM’s capability in tracking extreme market shifts. Transitioning to the second chapter, the focus shifts to the potentially influential realm of investor sentiment, seen as one of the many factors contributing to fat tails’ presence in return distributions. Building on insights from (Baker and Wurgler, 2007), we examine the potential impact of political speeches and daily briefings from 10 Downing Street during the COVID-19 crisis on market sentiment. Recognizing the profound market impact of such communications, the chapter seeks correlations between these briefings and market fluctuations. Employing advanced Natural Language Processing (NLP) techniques, this chapter harnesses the power of the Bidirectional Encoder Representations from Transformers (BERT) algorithm (Devlin et al., 2018) to extract sentiment from governmental communications. By comparing the derived sentiment scores with stock market indices’ performance metrics, potential relationships between public communications and market trajectories are unveiled. This approach represents a melding of traditional finance theory with state-of-the-art machine learning techniques, offering a fresh lens through which the dynamics of market behaviour can be understood in the context of external communications. In conclusion, this thesis provides an intricate examination of the IFBM model’s performance and the influence of investor sentiment, especially under crisis conditions. This exploration not only advances the discourse in behavioural finance but also underscores the pivotal role of sophisticated models in understanding and predicting market trajectories

Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included