Affine Diffusions with Non-Canonical State Space

Asset Pricing with Matrix Affine Jump Diffusions∗

This paper introduces a new class of matrix-valued affine jump diffusions that are convenient for modeling multivariate risk factors in many financial and econometric problems. We provide an analytical transform analysis for this class of models, leading to an analytical treatment of a broad class of multivariate valuation and econometric problems. Examples of potential applications include fix...

AN OBSERVER-BASED INTELLIGENT DECENTRALIZED VARIABLE STRUCTURE CONTROLLER FOR NONLINEAR NON-CANONICAL NON-AFFINE LARGE SCALE SYSTEMS

In this paper, an observer based fuzzy adaptive controller (FAC) is designed fora class of large scale systems with non-canonical non-affine nonlinear subsystems. It isassumed that functions of the subsystems and the interactions among subsystems areunknown. By constructing a new class of state observer for each follower, the proposedconsensus control method solves the problem of unmeasured sta...

Canonical Forms For State–Space Descriptions

Canonical Self - Affine Tilings

An iterated function system Φ consisting of contractive affine mappings has a unique attractor F ⊆ R which is invariant under the action of the system, as was shown by Hutchinson [Hut]. This paper shows how the action of the function system naturally produces a tiling T of the convex hull of the attractor. These tiles form a collection of sets whose geometry is typically much simpler than that ...

Fully non linear equations with integral diffusions

The authors establish weighted decay rates for the energy associated with the Cauchy problem { utt − div(b(x)∇u) + a(x)ut = 0, x ∈ R, t > 0 u(0, x) = u0(x), ut(0, x) = u1(x), x ∈ R. Such a system appears in models for traveling waves in a non-homogeneous gas with damping that changes with the position. This problem has been studied intensively for the homogeneous medium (when b is constant), bu...