Joerg Kampen
Determiniation of the homotopy class of maps on compact orientable surfaces of positive genus g with infinitely many periodic points (part I).
Tue, 06/15/2010 - 15:01 — SomNambulAuthors: Joerg Kampen
Subjects: Dynamical Systems
AbstractWe consider the homotopical dynamics on compact orientable surfaces of
positive genus g. We establish a sufficient and necessary algebraic criterion
for homotopy classes with infinitely many periodic points of maps on such
surfaces in terms of the characteristic polynomial of the matrix representing
the correspondig homomorphism of the first homology group.On a class of semi-elliptic diffusion models. Part I: a constructive analytical approach for global existence, densities, and numerical schemes (with applications to the Libor market model).
Mon, 03/01/2010 - 16:01 — SomNambulAuthors: Joerg Kampen, Christian Fries
Subjects: Analysis of PDEs
AbstractComputational parsimony makes reduced factor Libor market models popular
among practioners. However, value functions and sensitivities of such models
are described by degenerate parabolic (i.e. semielliptic) equations where the
existence of regular global solutions is not trivial. In this paper, we show
that for a considerable class of degenerate equations (including equations
corresponding to reduced LIBOR market models of practical interest) regular
global solutions can be constructed. The result is also of interest for the
theory of degenerate parabolic equations.Characteristic functions of affine processes via calculus of their operator symbols.
Tue, 02/16/2010 - 16:01 — SomNambulAuthors: Joerg Kampen
Subjects: Functional Analysis
AbstractThe characteristic functions of multivariate Feller processes with generator
of affine type, and with smooth symbol functions have an explicit
representation in terms of power series with rational number coefficients and
with monmoms consisting of powers of the the symbol functions and formal
derivatives of the symbol functions. The power series repesentations are
convergent globally in time and on bounded domains of arbitrary size.
Generalized symbol functions can be derived leading to power series expansions
which are convergent on arbitrary domains in special cases.On the multivariate Burgers equation and the incompressible Navier-Stokes equation.
Fri, 10/30/2009 - 16:01 — SomNambulAuthors: Joerg Kampen
Subjects: Analysis of PDEs
AbstractWe prove global existence of the multivariate viscous Burgers equation system
defined on the whole space or on a domain isomorphic to the $n$-torus and with
time horizon up to infinity and $C^{\infty}$- data (satisfying some growth
conditions if the problem is posed on the whole space). The proof is by a
semi-explicit perturbative expansion in transformed coordinates where the
convergence is guaranteed by certain a priori estimates.
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