This PhD thesis aims to study financial processes which have semi-heavy-tailed marginal distributions and may exhibit memory. The traditional Black-Scholes model is expanded to incorporate memory via an integral operator, resulting in a class of market models which still preserve the...

We construct a complete metric space (Y,dY) of measure-valued images, μ:X→M(Rg), where X is the base or pixel space and M(Rg) is the set of probability measures supported on the greyscale range Rg. Such a formalism is well-suited to nonlocal image processing, i.e., the manipulation of the...

The yuan-dollar returns prior to the 2005 revaluation show a Sierpinski triangle in an iterated function system clumpiness test. Yet the fractal vanishes after the revaluation. The Sierpinski commonly emerges in the chaos game, where randomness coexists with deterministic rules (M.F. Barnsley,...

This paper introduces the truncator map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify its periodic orbits using properties of endomorphisms of the...

In this paper some new contractive operators on C([a, b]) of IFS type arebuilt. Inverse problems are introduced and studied by convex optimizationproblems. A stability result and some optimality conditions are given.

In this paper we consider a class of nonparametric estimators of a distribution function F, with compact support, based on the theory of IFSs. The estimator of F is tought as the fixed point of a contractive operator T defined in terms of a vector of parameters p and a family of affine maps W...

Using nonlinear optimization techniques in fractal image compression. Fractal image compression generally seeks to express an image as a union of spatially contracted and greyscale modified copies of subsets of itself. Most practical as well as theoretical works in image processing and...