Extremal properties of evolving networks: local dependence and heavy tails

Extremal shot noises, heavy tails and max-stable random fields

We consider the extremal shot noise defined by M(y) = sup{mh(y − x); (x,m) ∈ Φ}, where Φ is a Poisson point process on R × (0,+∞) with intensity λdxG(dm) and h : R → [0,+∞] is a measurable function. Extremal shot noises naturally appear in extreme value theory as a model for spatial extremes and serve as basic models for annual maxima of rainfall or for coverage field in telecommunications. In ...

Extremal Properties of Complex Networks

We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph qualities for any arbitrary number of nodes and edges and analytically derive the form and properties of such networks.

Long Memory Dynamics for Multivariate Dependence under Heavy Tails

We develop a new simultaneous time series model for volatility and dependence with long memory (fractionally integrated) dynamics and heavy-tailed densities. Our new multivariate model accounts for typical empirical features in financial time series while being robust to outliers or jumps in the data. In the empirical study for four Dow Jones equities, we find that the degree of memory in the v...

Extremal problems for local properties of graphs

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...