Journal•ISSN: 0926-2601
Potential Analysis
Springer Science+Business Media
About: Potential Analysis is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Potential theory & Bounded function. It has an ISSN identifier of 0926-2601. Over the lifetime, 1501 publications have been published receiving 24391 citations.
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TL;DR: In this article, the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations was proved for the Ito formula.
Abstract: Since the fractional Brownian motion is not a semi-martingale, the usual Ito calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Ito formula, the Ito–Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.
713 citations
TL;DR: In this paper, the authors define Sobolev space W1,p for 1
Abstract: We define Sobolev space W1,p for 1
577 citations
TL;DR: In this article, the authors give some basic and important properties of typical Banach spaces of functions of G-Brownian motion paths induced by a sublinear expectation, which can be applied in continuous time dynamic and coherent risk measures in finance, in particular for path-dependence risky positions under situations of volatility model uncertainty.
Abstract: In this paper we give some basic and important properties of several typical Banach spaces of functions of G-Brownian motion paths induced by a sublinear expectation—G-expectation. Many results can be also applied to more general situations. A generalized version of Kolmogorov’s criterion for continuous modification of a stochastic process is also obtained. The results can be applied in continuous time dynamic and coherent risk measures in finance, in particular for path-dependence risky positions under situations of volatility model uncertainty.
514 citations
TL;DR: In this paper, a complete description of the eigenvalues of the Laplacian on the finite Sierpinski gasket is presented, and highly oscillatory behaviours of the distribution function of the Eigenvalues, the integrated density of states (for the infinite gasket) and the spectrum of the LPA on the infinite Gasket are demonstrated.
Abstract: A complete description of the eigenvalues of the Laplacian on the finite Sierpinski gasket is presented. We then demonstrate highly oscillatory behaviours of the distribution function of the eigenvalues, the integrated density of states (for the infinite gasket) and the spectrum of the Laplacian on the infinite gasket. The method has two ingredients: the decimation method in calculating eigenvalues due to Rammal and Toulouse and a simple description of the Dirichlet form associated with the Laplacian.
340 citations
TL;DR: In this article, the authors considered a class of pure jump Markov processes whose jump kernels are comparable to those of symmetric stable processes and established a Harnack inequality for nonnegative functions that are harmonic with respect to these processes.
Abstract: We consider a class of pure jump Markov processes in R
d
whose jump kernels are comparable to those of symmetric stable processes. We establish a Harnack inequality for nonnegative functions that are harmonic with respect to these processes. We also establish regularity for the solutions to certain integral equations.
280 citations