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With Andrzej Lasota There and Back Again

Annales Mathematicae Silesianae
The paper below is a written version of the 17th Andrzej Lasota Lecture presented on January 12th, 2024 in Katowice. During the lecture we tried to show the impact of Andrzej Lasota’s results on the author’s research concerning various fields of ...
Rudnicki Ryszard
doaj   +1 more source

A map with invariant Cantor set of positive measure

, 2005
Many examples exist of one-dimensional systems that are topologically conjugate to the shift operator on Σ2 and are thus chaotic. Most of these examples which have invariant Cantor subsets, have Cantor subsets of measure zero.
Murdock, J., Botelho, F.
core   +1 more source

Periodic and invariant measures for stochastic wave equations

Electronic Journal of Differential Equations, 2004
We establish the existence of periodic and invariant measures for a semilinear wave equation with random noise. These are counterparts of time-periodic and stationary solutions of a deterministic equation. The key element in our analysis is to prove that
Jong Uhn Kim
doaj  

Density Formula in Malliavin Calculus by Using Stein’s Method and Diffusions

Mathematics
Let G be a random variable of functionals of an isonormal Gaussian process X defined on some probability space. Studies have been conducted to determine the exact form of the density function of the random variable G.
Hyun-Suk Park
doaj   +1 more source

Invariant Gibbs measure for Anderson NLW

, 2023
We study the Gaussian measure whose covariance is related to the Anderson Hamiltonian operator, proving that it admits a regular coupling to the (standard) Gaussian free field exploiting the stochastic optimal control formulation of Gibbs measures. Using
Barashkov, Nikolay, De Vecchi, Francesco C., Zachhuber, Immanuel   +2 more
core  

Higher d Eisenstein series and a duality-invariant distance measure

Journal of High Energy Physics
The Petersson inner product is a natural inner product on the space of modular invariant functions. We derive a formula, written as a convergent sum over elementary functions, for the inner product E s (G, B) of the real analytic Eisenstein series $${E}_{
Nathan Benjamin, A. Liam Fitzpatrick
doaj   +1 more source

Ergodicity of the two-dimensional magnetic Benard problem

Electronic Journal of Differential Equations, 2016
We study the two-dimensional magnetic Benard problem with noise, white in time. We prove the well-posedness including the path-wise uniqueness of the generalized solution, and the existence of the unique invariant, and consequently ergodic, measure ...
Kazuo Yamazaki
doaj  

Arclength as the invariant measure for an ifs with probabilities

, 2015
Given a continuous rectifiable function (Formula presented.), we present a simple Iterated Function System (IFS) with probabilities whose invariant measure is the normalized arclength measure on the graph of (Formula presented.)
D. La Torre, F. Mendivil
core   +1 more source

Path integral measures and diffeomorphism invariance

Journal of High Energy Physics
Much like the action, diffeomorphism invariance can be used to fix the form of the path integral measure in quantum gravity. Moreover, since there is a redundancy between what constitutes “the action” and what constitutes “the measure” one can always ...
Alfio Bonanno, Kevin Falls, Renata Ferrero   +2 more
doaj   +1 more source

On invariant probability measures I [PDF]

Pacific Journal of Mathematics, 1960
Blum, J. R., Hanson, D. L.
openaire   +5 more sources