On some Fourier aspects of the construction of certain Wiener integrals

AbstractThe existence and best L2-bounds for the Wiener type integrals ∫01f(s)dXs, where X ranges through a wide class of Bessel-like centered processes, and f belongs to L2([0,1]), are discussed in terms of Fourier transforms associated with some characteristics of X, thus providing some unification of previous results on this topic obtained by the authors [T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered powers of Bessel processes, I, Markov Processes and their Related Fields (2006) (in press), T. Funaki, Y. Hariya, F. Hirsch, M. Yor, On the construction of Wiener integrals with respect to certain pseudo-Bessel processes, Stochastic Processes and their Applications (2006) (in press)] as well as yielding new results

On the construction of Wiener integrals with respect to certain pseudo-Bessel processes

In previous papers [T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered powers of Bessel processes, I, Markov Processes Related Fields (2006) (in press); T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered Bessel and related processes, II, Alea (2006) (in press)], the authors have shown that it is possible to define the Wiener-type integrals , for every and any centered Bessel process with dimension d>1. In this paper, various conditions are stated, showing that such a construction is possible for a large class of processes indexed by two square integrable Brownian functionals. In particular, some of the results previously obtained for the Bessel processes are thus recovered, and in fact shown to extend to certain processes of the form .Bessel processes Ito's representation theorem Wiener integrals Scaling property Gebelein's inequality Hermite and Laguerre series expansions

On some Fourier aspects of the construction of certain Wiener integrals

The existence and best L2-bounds for the Wiener type integrals , where X ranges through a wide class of Bessel-like centered processes, and f belongs to L2([0,1]), are discussed in terms of Fourier transforms associated with some characteristics of X, thus providing some unification of previous results on this topic obtained by the authors [T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered powers of Bessel processes, I, Markov Processes and their Related Fields (2006) (in press), T. Funaki, Y. Hariya, F. Hirsch, M. Yor, On the construction of Wiener integrals with respect to certain pseudo-Bessel processes, Stochastic Processes and their Applications (2006) (in press)] as well as yielding new results.Wiener integrals Quadratic forms Tempered distributions Optimal bounds

Mixing behavior in quaternary garnet solid solution and an extended Ellis and Green garnet-clinopyroxene geothermometer

Applications of the different formulations of garnet-clinopyroxene geothermometers to crustal granulites and particularly to metamorphosed manganese formations show a wide scatter of estimates. This is primarily related to the uncertainty associated with the formulation of the activity-composition relationship in garnet solid solution besides that in the clinopyroxene solid solution. The largest uncertainty appears to have resulted from the adopted Mg-Mn interaction parameter in garnet which is yet to be experimentally determined. A fresh statistical regression of eleven pairs of garnet and clinopyroxene equilibrated at identical P-T conditions from a manganese formation in India yields WMg-MnGt (=WMn-Mg) value of 1600±500 cal/mols. An extension of the Ellis and Green (1979) geothermometer, known to work well in normal granulites, incorporating terms associated with the activity coefficients of the exchangeable cations, now yields consistent temperature estimation from normal granulites as well as from metamorphosed manganese formations. The geothermometer, however, will not work well for garnet having XFe≥0.65 and clinopyroxenes containing appreciable Na, Al and/or Fe3+

Fenomena Cyber Religion Sebagai Ekspresi Keberagamaan Di Internet Pada Komunitas Shift (Cyber Religion Phenomenon as A Religious Expression on the Internet in the Shift Community)

This article aims to determine the form of Shift's religious expression and the factor of the Shift community's interest in the context of cyberreligion. The research method is qualitative with the type of phenomenological research. There are 5 research subjects (subscribers) and the research object of the YouTube channel Shift. The interactive model analysis technique of Miles & Huberman from the results of data collection that the authors get. The results showed that the phenomenon of cyberreligion has touched various circles and was used by Ust. Hanan Attaki by establishing a Shift which targets the younger generation in the form of online religion. The use of YouTube as a means of spreading Shift's da'wah is categorized into the File-Sharing category. The study, which is nicely packaged by Ust. Hanan Attaki, has made it loved by the younger generation as an alternative in their religious information