2004, ISBN: 9781402024962

[ED: Hardcover], [PU: Springer Netherlands], This book develops the potential theory starting from a sub-Markovian resolvent of kernels on a measurable space, covering the context offered… Meer...

[ED: Hardcover], [PU: Springer Netherlands], This book develops the potential theory starting from a sub-Markovian resolvent of kernels on a measurable space, covering the context offered by a right process with general state space. It turns out that the main results from the classical cases (e.g., on locally compact spaces, with Green functions) have meaningful extensions to this setting. The study of the strongly supermedian functions and specific methods like the Revuz correspondence, for the largest class of measures, and the weak duality between two sub-Markovian resolvents of kernels are presented for the first time in a complete form. It is shown that the quasi-regular semi-Dirichlet forms fit in the weak duality hypothesis. Further results are related to the subordination operators and measure perturbations. The subject matter is supplied with a probabilistic counterpart, involving the homogeneous random measures, multiplicative, left and co-natural additive functionals. The book is almost self-contained, being accessible to graduate students. The developmentsin the recent yearsof the potential theoryemphasized a classof functions larger than that of excessive functions (i.e. the positive superharmonic functionsfromtheclassicalpotentialtheoryassociatedwiththeLaplaceoperator), namely the strongly supermedian functions. It turns out that a positive Borel function will be strongly supermedian if and only if it is the in?mum of all its excessive majorants. Apparently, these functions have been introduced by J.F. Mertens and then they have been studied mainly by P.A. Meyer, G. Mokobodzki, D. Feyel and recently by P.J. Fitzsimmons and R.K. Getoor. The aimofthis bookisamongothersto developa potential theoryappropriate to this new class of functions. Although our methods are analytical, we present also the probabilistic counterparts from the Markov processes theory. The natural frame in which this theory is settled is given by a sub-Markovian resolvent of kernels on a Radon measurable space. After a possible extension of the space, such a resolvent becomes that one associated with a right process on a Radon topological space, not necessary locally compact and without existing a reference measure. Intimately related to the excessive functions we present certain basic tools of the theory: the Ray topology and compacti?cation, the ?ne carrier and the reduction operation on measurable sets. We examine di?erent types of negligible sets with respect to a ?nite measure ?:the ?-polar, ?-semipolar and ?-mince sets. We take advantage of the cone of potentials structure for both excessive functions and measures. 2004. vi, 370 S. VI, 370 p. 235 mm Versandfertig in 2-4 Wochen, DE, [SC: 0.00], Neuware, gewerbliches Angebot, offene Rechnung (Vorkasse vorbehalten)<

ISBN: 9781402024962

The developmentsin the recent yearsof the potential theoryemphasized a classof functions larger than that of excessive functions (i. e. the positive superharmonic functionsfromtheclassica… Meer...

The developmentsin the recent yearsof the potential theoryemphasized a classof functions larger than that of excessive functions (i. e. the positive superharmonic functionsfromtheclassicalpotentialtheoryassociatedwiththeLaplaceoperator), namely the strongly supermedian functions. It turns out that a positive Borel function will be strongly supermedian if and only if it is the in?mum of all its excessive majorants. Apparently, these functions have been introduced by J. F. Mertens and then they have been studied mainly by P. A. Meyer, G. Mokobodzki, D. Feyel and recently by P. J. Fitzsimmons and R. K. Getoor. The aimofthis bookisamongothersto developa potential theoryappropriate to this new class of functions. Although our methods are analytical, we present also the probabilistic counterparts from the Markov processes theory. The natural frame in which this theory is settled is given by a sub-Markovian resolvent of kernels on a Radon measurable space. After a possible extension of the space, such a resolvent becomes that one associated with a right process on a Radon topological space, not necessary locally compact and without existing a reference measure. Intimately related to the excessive functions we present certain basic tools of the theory: the Ray topology and compacti?cation, the ?ne carrier and the reduction operation on measurable sets. We examine di?erent types of negligible sets with respect to a ?nite measure ?:the ?-polar, ?-semipolar and ?-mince sets. We take advantage of the cone of potentials structure for both excessive functions and measures. | Potential Theory and Right Processes by Lucian Beznea Hardcover | Indigo Chapters Books > Science & Nature > Math & Physics > Mathematics P10117, Lucian Beznea<

ISBN: 9781402024962

Hardback, [PU: Springer-Verlag New York Inc.], Develops the potential theory starting from a sub-Markovian resolvent of kernels on a measurable space, covering the context offered by a ri… Meer...

Hardback, [PU: Springer-Verlag New York Inc.], Develops the potential theory starting from a sub-Markovian resolvent of kernels on a measurable space, covering the context offered by a right process with general state space. It is shown that the quasi-regular semi-Dirichlet forms fit in the weak duality hypothesis., Mathematics, Calculus & Mathematical Analysis, Calculus, Probability & Statistics, Applied Mathematics, Stochastics, Maths For Scientists<

2004, ISBN: 9781402024962

2004 ed., Hardcover, Buch, [PU: Springer-Verlag New York Inc.]