Affine processes are regular

We show that stochastically continuous, time-homogeneous affine processes on the canonical state space \Rplus^m \times \RR^n are always regular. In the paper of \citet{Duffie2003} regularity was used as a crucial basic assumption. It was left open whether this regularity condition is automatically satisfied, for stochastically continuous affine processes. We now show that the regularity assumption is indeed superfluous, since regularity follows from stochastic continuity and the exponentially affine behavior of the characteristic function. For the proof we combine classic results on the differentiability of transformation semigroups with the method of the moving frame which has been recently found to be useful in the theory of SPDEs

Regularity of affine processes on general state spaces

We consider a stochastically continuous, affine Markov process in the sense of Duffie, Filipovic and Schachermayer, with cadlag paths, on a general state space D, i.e. an arbitrary Borel subset of R^d. We show that such a process is always regular, meaning that its Fourier-Laplace transform is differentiable in time, with derivatives that are continuous in the transform variable. As a consequence, we show that generalized Riccati equations and Levy-Khintchine parameters for the process can be derived, as in the case of $D = R_+^m \times R^n$ studied in Duffie, Filipovic and Schachermayer (2003). Moreover, we show that when the killing rate is zero, the affine process is a semi-martingale with absolutely continuous characteristics up to its time of explosion. Our results generalize the results of Keller-Ressel, Schachermayer and Teichmann (2011) for the state space $R_+^m \times R^n$ and provide a new probabilistic approach to regularity.Comment: minor correction

Reference data for phase diagrams of triangular and hexagonal bosonic lattices

We investigate systems of bosonic particles at zero temperature in triangular and hexagonal optical lattice potentials in the framework of the Bose-Hubbard model. Employing the process-chain approach, we obtain accurate values for the boundaries between the Mott insulating phase and the superfluid phase. These results can serve as reference data for both other approximation schemes and upcoming experiments. Since arbitrary integer filling factors g are amenable to our technique, we are able to monitor the behavior of the critical hopping parameters with increasing filling. We also demonstrate that the g-dependence of these exact parameters is described almost perfectly by a scaling relation inferred from the mean-field approximation.Comment: 6 pages, 5 figures, accepted for publication in EP

Affine processes are regular

We show that stochastically continuous, time-homogeneous affine processes on the canonical state space $${\mathbb{R}_{\geq 0}^m \times \mathbb{R}^n}$$ are always regular. In the paper of Duffie etal. (Ann Appl Probab 13(3):984-1053, 2003) regularity was used as a crucial basic assumption. It was left open whether this regularity condition is automatically satisfied for stochastically continuous affine processes. We now show that the regularity assumption is indeed superfluous, since regularity follows from stochastic continuity and the exponentially affine form of the characteristic function. For the proof we combine classic results on the differentiability of transformation semigroups with the method of the moving frame which has been recently found to be useful in the theory of SPDE

Transient band structures in the ultrafast demagnetization of ferromagnetic gadolinium and terbium

We compare the laser-driven demagnetization dynamics of the rare earths gadolinium and terbium by mapping their transient valance band structures with time- and angle-resolved photoelectron spectroscopy. In both metals, the minority and majority spin valence bands evolve independently with different time constants after optical excitation. The ultrafast shift of the partially unoccupied minority spin bulk band to higher binding energy and of the majority spin surface state to lower binding energy suggests spin transport between surface and bulk. The slower response of the fully occupied majority spin band follows the lattice temperature and is attributed to Elliott-Yafet type spin-flip scattering. Terbium shows a stronger and faster decay of the exchange splitting, pointing to ultrafast magnon emission via 4f spin-to- lattice coupling

Fluence-dependent dynamics of the 5d6s exchange splitting in Gd metal after femtosecond laser excitation

We investigate the fluence-dependent dynamics of the exchange-split 5d6s valence bands of Gd metal after femtosecond, near-infrared (IR) laser excitation. Time- and angle-resolved photoelectron spectroscopy (tr-ARPES) with extreme ultraviolet (XUV) probe pulses is used to simultaneously map the transient binding energies of the minority and majority spin valence bands. The decay constant of the exchange splitting increases with fluence. This reflects the slower response of the occupied majority-spin component, which we attribute to Elliot–Yafet spin-flip scattering in accordance with the microscopic three-temperature model (M3TM). In contrast, the time constant of the partly unoccupied minority-spin band stays unaffected by a change in pump fluence. Here, we introduce as an alternative to superdiffusive spin transport exchange scattering, which is an ultrafast electronic mechanism explaining the observed dynamics. Exchange scattering can reduce the spin polarization in the partially unoccupied minority-spin band and thus its energetic position without effective demagnetization

Polynomial processes and their applications to mathematical finance

We introduce a class of Markov processes, called m-polynomial, for which the calculation of (mixed) moments up to order m only requires the computation of matrix exponentials. This class contains affine processes, processes with quadratic diffusion coefficients, as well as Lévy-driven SDEs with affine vector fields. Thus, many popular models such as exponential Lévy models or affine models are covered by this setting. The applications range from statistical GMM estimation procedures to new techniques for option pricing and hedging. For instance, the efficient and easy computation of moments can be used for variance reduction techniques in Monte Carlo method