Indore (Madhya Pradesh): A groundbreaking study co-authored by Prof Aditya Maheshwari of the Indian Institute of Management-Indore has introduced a powerful new mathematical framework for modelling real-world events that unfold with self-exciting behaviour, a phenomenon seen in financial markets, cybersecurity, seismic activity and even social media virality.
The study, titled “Tempered Fractional Hawkes Process and its Generalizations,” was published in the prestigious ‘Journal of Mathematical Analysis and Applications’.
The study marks a significant theoretical advancement in the design and understanding of mathematical processes used to explain how events occur and influence one another over time.
The research builds on the well-known Hawkes process, a model in which one event increases the likelihood of subsequent events, much like a market crash triggering further volatility or an online post sparking additional engagement.
The authors have introduced the generalized fractional Hawkes process (GFHP) by time-changing the classical Hawkes process using an inverse Lévy subordinator, thereby incorporating fractional dynamics into the model. Crucially, the paper derives the mean, variance, covariance and fractional difference, differential equations governing the newly proposed Tempered Fractional Hawkes Process (TFHP). It also presents simulated sample paths comparing the classical Hawkes process with its tempered fractional variant.
The implications of this research stretch across multiple high-stakes sectors. In finance, the TFHP can enhance predictions of market volatility and abrupt trading activity.
In cybersecurity, it can more accurately model cascading attacks or breach attempts. Supply chain managers can use it to anticipate disruptive events, while researchers working with high-frequency or self-triggering data such as algorithmic trading platforms and real-time fraud detection systems stand to gain from the framework’s improved realism.
By incorporating a tempered approach, the model ensures that the influence of past events fades over time, preventing overestimation of long-term impacts and enabling more precise calibration in practical applications.
