Search

Area‐restricted search is the capacity to change search effort adaptively in response to resource encounters or expectations, from directional exploration (global, extensive search) to focused exploitation (local, intensive search). This search pattern is used by numerous organisms, from worms and insects to humans, to find various targets, such as food, mates, nests, and other resources. Area‐restricted search has been studied for at least 80 years by ecologists, and more recently in the neurological and psychological literature. In general, the conditions promoting this search pattern are: (1) clustered resources; (2) active search (e.g. not a sit‐and‐wait predator); (3) searcher memory for recent target encounters or expectations; and (4) searcher ignorance about the exact location of targets. Because area‐restricted search adapts to resource encounters, the search can be performed at multiple spatial scales. Models and experiments have demonstrated that area‐restricted search is superior to alternative search patterns that do not involve a memory of the exact location of the target, such as correlated random walks or Lévy walks/flights. Area‐restricted search is triggered by sensory cues whereas concentrated search in the absence of sensory cues is associated with other forms of foraging. Some neural underpinnings of area‐restricted search are probably shared across metazoans, suggesting a shared ancestry and a shared solution to a common ecological problem of finding clustered resources. Area‐restricted search is also apparent in other domains, such as memory and visual search in humans, which may indicate an exaptation from spatial search to other forms of search. Here, we review these various aspects of area‐restricted search, as well as how to identify it, and point to open questions. [ABSTRACT FROM AUTHOR]

"Stable Lévy Processes via Lamperti-Type Representations" by Andreas E. Kyprianou and Juan Carlos Pardo is a comprehensive exploration of stable Lévy processes and their connection to self-similar Markov processes. The book covers topics such as distributional stability, Lévy processes, the Wiener-Hopf factorization, and stable processes. It also delves into hypergeometric Lévy processes, positive self-similar Markov processes, and the distribution and extrema of stable processes. The authors provide explicit fluctuation identities and explore the relationships between self-similarity and stable processes. This book is recommended for researchers and can be used as material for a graduate course. [Extracted from the article]

The Lévy-driven affine short rate models follow and a chapter on the completeness of the presented Lévy term structure models concludes. In conclusion, the book by M. Barski and J. Zabczyk on modelling fixed income markets based on Lévy processes is a textbook that fills perfectly a gap in the existing mathematical finance literature. The applications of Lévy processes in mathematical finance go back to the seminal paper of Merton ([4]), entitled "Option pricing when underlying stock returns are discontinuous", which galvanized the research landscape on Lévy models with respect to financial applications. [Extracted from the article]

The article reviews the book "Lévy Processes" by Jean Bertoin.

The article reviews the book "Introductory Lectures on Fluctuations of Lévy Processes With Applications," by Andreas E. Kyprianou.