Sample path properties of stochastic processes represented as multiple stable integrals

Originally published as a technical report no. 871, October 1989 for Cornell University Operations Research and Industrial Engineering. Available online: http://hdl.handle.net/1813/8754This paper studies the sample path properties of stochastic processes represented by multiple symmetric α-stable integrals. It relates the “smoothness” of the sample paths to the “smoothness” of the (non-random) integrand. It also contains results about the behavior of the distribution of suprema and zero-one laws

General inverse problems for regular variation

Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components of the original random structure. In this paper we build up on previous work and derive results in the multivariate case and in situations where regular variation is not restricted to one particular direction or quadrant

On the origin of cavities in extraterrestrial magnetic spherules

It was discovered that extraterrestrial magnetic spherules larger than 10 μm in diameter contain internal cavities. The possible origin of cavities is discussed. It is suggested that the primary particles contain ferrous carbonate or ferric hydroxide that upon heating during entry of micrometeorite releases carbon dioxide or water vapor that produces cavity in the molten spherule. The chemical composition of magnetic spherules is similar to that of the crust of the Earth

Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes

In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes. We also show that a fractional Brownian motion and the related Riemann-Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of our large deviation estimates, we derive laws of iterated logarithm for the corresponding local times. The key points of our methods: (1) logarithmic superadditivity of a normalized sequence of moments of exponentially randomized local time of a fractional Brownian motion; (2) logarithmic subadditivity of a normalized sequence of moments of exponentially randomized intersection local time of Riemann-Liouville processes; (3) comparison of local and intersection local times based on embedding of a part of a fractional Brownian motion into the reproducing kernel Hilbert space of the Riemann-Liouville process.Comment: To appear in the Annals of Probabilit

Spectral representation and structure of self-similar processes

In this paper we establish a spectral representation of any symmetric stable self-similar process in terms of multiplicative flows and cocycles. Applying the Lamperti transformation we obtain a unique decomposition of a symmetric stable self-similar process into three independent parts: mixed fractional motion, harmonizable and evanescent.Self-similar process; Stable distribution; Lamperti transformation;

Sample path properties of stochastic processes represented as multiple stable integrals

AbstractThis paper studies the sample path properties of stochastic processes represented by multiple symmetric α-stable integrals. It relates the “smoothness” of the sample paths to the “smoothness” of the (non-random) integrand. It also contains results about the behavior of the distribution of suprema and zero-one laws

Nanostructured targets for TNSA laser ion acceleration

Abstract Nanostructured targets, based on hydrogenated polymers with embedded nanostructures, were prepared as thin micrometric foils for high-intensity laser irradiation in TNSA regime to produce high-ion acceleration. Experiments were performed at the PALS facility, in Prague, by using 1315 nm wavelength, 300 ps pulse duration and an intensity of 1016 W/cm2 and at the IPPLM, in Warsaw, by using 800 nm wavelength, 40 fs pulse duration, and an intensity of 1019 W/cm2. Forward plasma diagnostic mainly uses SiC detectors and ion collectors in time of flight (TOF) configuration. At these intensities, ions can be accelerated at energies above 1 MeV per nucleon. In presence of Au nanoparticles, and/or under particular irradiation conditions, effects of resonant absorption can induce ion acceleration enhancement up to values of the order of 4 MeV per nucleon