Delay differential equations driven by Levy processes: stationarity and Feller properties

We consider a stochastic delay differential equation driven by a general Levy process. Both, the drift and the noise term may depend on the past, but only the drift term is assumed to be linear. We show that the segment process is eventually Feller, but in general not eventually strong Feller on the Skorokhod space. The existence of an invariant measure is shown by proving tightness of the segments using semimartingale characteristics and the Krylov-Bogoliubov method. A counterexample shows that the stationary solution in completely general situations may not be unique, but in more specific cases uniqueness is established.Comment: 28 page

Alien Registration- Riedle, Elizabeth M. (Portland, Cumberland County)

https://digitalmaine.com/alien_docs/21594/thumbnail.jp

Alien Registration- Riedle, Elizabeth M. (Portland, Cumberland County)

https://digitalmaine.com/alien_docs/21594/thumbnail.jp

Variational solutions of stochastic partial differential equations with cylindrical Levy noise

In this article, the existence of a unique solution in the variational approach of the stochastic evolution equation \dX(t) = F(X(t)) \dt + G(X(t)) \dL(t) driven by a cylindrical L\'evy process $L$ is established. The coefficients $F$ and $G$ are assumed to satisfy the usual monotonicity and coercivity conditions. The noise is modelled by a cylindrical L\'evy processes which is assumed to belong to a certain subclass of cylindrical L\'evy processes and may not have finite moments.Comment: Completely revised version, removed some inconsistencies and inaccuracie

Electronic spectra of polyatomic molecules with resolved individual rotational transitions

The density of rotational transitions for a polyatomic molecule is so large that in general many such transitions are hidden under the Doppler profile, this being a fundamental limit of conventional high resolution electronic spectroscopy. We present here the first Doppler-free cw two-photon spectrum of a polyatomic molecule. In the case of benzene, 400 lines are observed of which 300 are due to single rotational transitions, their spacing being weil below the Doppler profile. The resolution so achieved is 1.5 X 10'. Benzene is a prototype planar molecule taken to have D •• symmetry in the ground as weil as in the first excited state. From our ultra-high resolution results it is found that benzene in the excited SI state i8 a symmetrical rotor to a high degree. A negative inertial defect is found for the excited state. The origin of this inertial defect is discused

Attosecond control of electron dynamics in carbon monoxide

Laser pulses with stable electric field waveforms establish the opportunity to achieve coherent control on attosecond timescales. We present experimental and theoretical results on the steering of electronic motion in a multi-electron system. A very high degree of light-waveform control over the directional emission of C+ and O+ fragments from the dissociative ionization of CO was observed. Ab initio based model calculations reveal contributions to the control related to the ionization and laser-induced population transfer between excited electronic states of CO+ during dissociation

Vibronic excitations of large molecules in solution studied by two-color pump–probe experiments on the 20 fs time scale

The ultrafast vibronic response of organic dye molecules in solution is studied in pump–probe experiments with 30 fs excitation pulses resonant to S0–Sn transitions. The molecular dynamics is probed either by pulses at the same spectral position or by 20 fs pulses overlapping with both the S0–S1 absorption and emission bands. Three contributions on distinctly different time scales are observed in the temporally and spectrally resolved two-color measurements. In the regime below 50 fs, a strong coherent coupling of the S0–Sn and the S0–S1 transitions occurs that is due to coherent vibrational motions in the electronic ground state. This signal is superimposed on the fast bleaching of the electronic ground state, resulting in a steplike increase of transmission. In the range of the S0–S1 emission band, one finds a subsequent picosecond rise of transmission that is due to stimulated emission from vibronic S1 states. The data demonstrate that the relaxation of Sn states directly populated by the pump pulses is much faster than the buildup of stimulated emission. This gives insight into different steps of intramolecular vibronic redistribution and is compared to the Sn–S1 relaxation in other molecules