Related papers: Spectral term structure models
This paper advances interest rate modeling in the post-LIBOR era by introducing rough stochastic volatility into the Forward Market Model (FMM). We establish a rigorous asymptotic expansion of swaption implied volatility, connecting the FMM…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
In this survey, we review how the global structure of the stable homotopy category gives rise to the chromatic filtration. We then discuss computational tools used in the study of local chromatic homotopy theory, leading up to recent…
In this paper we describe ideas about the string landscape, and how to relate it to the physics of the Standard Model of particle physics. First, we give a short status report about heterotic string compactifications. Then we focus on the…
We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category. The method is based on systematic localization, in Hirschhorn's sense, of a…
We introduce a model for simulating mutation of prokaryote DNA sequences. Using that model we can then evaluated traditional techniques like parsimony and maximum likelihood methods for computing phylogenetic relationships. We also use the…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…
The evolution of states of a spatial ecological model is studied. The model describes an infinite population of point entities placed in $\mathbb{R}^d$ which reproduce themselves at distant points (disperse) and die with rate that includes…
We consider an evolution system describing the phenomenon of marble sulphation of a monument, accounting of the surface rugosity. We first prove a local in time well posedness result. Then, stronger assumptions on the data allow us to…
A new language model for speech recognition is presented. The model develops hidden hierarchical syntactic-like structure incrementally and uses it to extract meaningful information from the word history, thus complementing the locality of…
For groups of prime order, equivariant stable maps between equivariant representation spheres are investigated using the Borel cohomology Adams spectral sequence. Features of the equivariant stable homotopy category, such as stability and…
We studied the formation of complex patterns using a variational principle and a standard energy functional. These patterns evolve by letting the system to search for the optimal configuration of a high conductivity channel, that in one…
We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
We revisit previously developed analytic models for defect evolution and adapt them appropriately for the study of semilocal string networks. We thus confirm the expectation (based on numerical simulations) that linear scaling evolution is…
Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…
"What are the origins of risks?" and "How material are they?" -- these are the two most fundamental questions of any risk analysis. Quantitative Structuring -- a technology for building financial products -- provides economically meaningful…
We develop unified theory and methodology for the inference of evolutionary Fourier power spectra for a general class of locally stationary and possibly nonlinear processes. In particular, simultaneous confidence regions (SCR) with…