منابع مشابه
Entropy Measures vs. Kolmogorov Complexity
Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for Rényi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we s...
متن کاملMartingale problems for some degenerate Kolmogorov equations
We obtain Calderón-Zygmund estimates for some degenerate equations of Kolmogorov type with inhomogeneous nonlinear coefficients. We then derive the well-posedness of the martingale problem associated with related degenerate operators, and therefore uniqueness in law for the corresponding stochastic differential equations. Some density estimates are established as well.
متن کاملSharp Asymptotics of the Kolmogorov Entropy for Gaussian Measures
Let U denote the unit ball of the Cameron-Martin space of a Gaussian measure on a Hilbert space. The sharp asymptotics for the Kolmogorov (metric) entropy numbers of U is derived. The condition imposed is regular variation of the eigenvalues of the covariance operator. A consequence is a precise link including constants to the functional quantiza-tion problem.
متن کاملFrom Gauss to Kolmogorov: Localized Measures of Complexity for Ellipses
The Gaussian width is a fundamental quantity in probability, statistics and geometry, known to underlie the intrinsic difficulty of estimation and hypothesis testing. In this work, we show how the Gaussian width, when localized to any given point of an ellipse, can be controlled by the Kolmogorov width of a set similarly localized. This connection leads to an explicit characterization of the es...
متن کاملKolmogorov Equations in Physics and in Finance
This paper contains a survey of results about linear and nonlinear partial differential equations of Kolmogorov type arising in physics and in mathematical finance. Some recent pointwise estimates proved in collaboration with S. Polidoro are also presented. Mathematics Subject Classification (2000). AMS Subject Classification: 35K57, 35K65, 35K70.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Evolution Equations
سال: 2008
ISSN: 1424-3199,1424-3202
DOI: 10.1007/s00028-008-0335-1