Matches in SemOpenAlex for { <https://semopenalex.org/work/W173976193> ?p ?o ?g. }
Showing items 1 to 66 of
66
with 100 items per page.
- W173976193 abstract "We consider a Markov chain ${X_n}_{n=1}^{infty}$ on $mathbb{R}^d$ defined by the stochastic recursion $X_n =M_n X_{n-1}+Q_n$ where $(Q_n,M_n)$ are i.i.d. random variables which take values in the affine group of the vector space $mathbb{R}^d$. Under natural hypothesis on $(Q_n,M_n)$, including negativity of the dominant Lyapunov exponent of the product of the matrices $M_n$, the transition operator $P$ of the chain has a unique stationary measure $eta$ and it is known that $eta$ is $alpha$-homogeneous at infinity for some $alpha>0$ depending on the law of $M_n$. We show spectral gap properties for $P$ and for a class of Fourier operators $P_v (vin mathbb{R}^d)$, on function spaces on $mathbb{R}^d$ of H{o}lder type. If $d>1$, we consider the Birkhoff sums $S_n= sum_{k=0}^n X_k$ and we show that the normalized sums converge to a normal law ($alphageq 2$) or to an $alpha$-stable law $(alpha<2)$ on $ mathbb{R}^d$, and these laws are fully non-degenerate. For $d=1$ such results were first obtained in Guivarc'h and Le Page(2008). Here we describe their natural extension to the general multidimensional setting. The corresponding analysis of the characteristic function of $S_n$ is based on the spectral gap properties of $P_v$ and on the homogeneity at infinity of $eta$ and of a family of companion measures $eta_v$." @default.
- W173976193 created "2016-06-24" @default.
- W173976193 creator A5007172280 @default.
- W173976193 creator A5045806343 @default.
- W173976193 creator A5091888401 @default.
- W173976193 date "2011-08-23" @default.
- W173976193 modified "2023-10-18" @default.
- W173976193 title "Spectral gap properties and convergence to stable laws for affine random walks on $mathbb{R}^d$" @default.
- W173976193 hasPublicationYear "2011" @default.
- W173976193 type Work @default.
- W173976193 sameAs 173976193 @default.
- W173976193 citedByCount "0" @default.
- W173976193 crossrefType "posted-content" @default.
- W173976193 hasAuthorship W173976193A5007172280 @default.
- W173976193 hasAuthorship W173976193A5045806343 @default.
- W173976193 hasAuthorship W173976193A5091888401 @default.
- W173976193 hasConcept C105795698 @default.
- W173976193 hasConcept C121194460 @default.
- W173976193 hasConcept C121332964 @default.
- W173976193 hasConcept C121864883 @default.
- W173976193 hasConcept C134306372 @default.
- W173976193 hasConcept C162324750 @default.
- W173976193 hasConcept C17744445 @default.
- W173976193 hasConcept C199539241 @default.
- W173976193 hasConcept C202444582 @default.
- W173976193 hasConcept C2777303404 @default.
- W173976193 hasConcept C2778114796 @default.
- W173976193 hasConcept C2985906921 @default.
- W173976193 hasConcept C33923547 @default.
- W173976193 hasConcept C44870925 @default.
- W173976193 hasConcept C50522688 @default.
- W173976193 hasConcept C92757383 @default.
- W173976193 hasConceptScore W173976193C105795698 @default.
- W173976193 hasConceptScore W173976193C121194460 @default.
- W173976193 hasConceptScore W173976193C121332964 @default.
- W173976193 hasConceptScore W173976193C121864883 @default.
- W173976193 hasConceptScore W173976193C134306372 @default.
- W173976193 hasConceptScore W173976193C162324750 @default.
- W173976193 hasConceptScore W173976193C17744445 @default.
- W173976193 hasConceptScore W173976193C199539241 @default.
- W173976193 hasConceptScore W173976193C202444582 @default.
- W173976193 hasConceptScore W173976193C2777303404 @default.
- W173976193 hasConceptScore W173976193C2778114796 @default.
- W173976193 hasConceptScore W173976193C2985906921 @default.
- W173976193 hasConceptScore W173976193C33923547 @default.
- W173976193 hasConceptScore W173976193C44870925 @default.
- W173976193 hasConceptScore W173976193C50522688 @default.
- W173976193 hasConceptScore W173976193C92757383 @default.
- W173976193 hasLocation W1739761931 @default.
- W173976193 hasLocation W1739761932 @default.
- W173976193 hasOpenAccess W173976193 @default.
- W173976193 hasPrimaryLocation W1739761931 @default.
- W173976193 hasRelatedWork W1597743604 @default.
- W173976193 hasRelatedWork W2038723108 @default.
- W173976193 hasRelatedWork W2089616341 @default.
- W173976193 hasRelatedWork W2755288388 @default.
- W173976193 hasRelatedWork W2797228403 @default.
- W173976193 hasRelatedWork W2949571925 @default.
- W173976193 hasRelatedWork W2963410169 @default.
- W173976193 hasRelatedWork W3103885756 @default.
- W173976193 hasRelatedWork W4297449606 @default.
- W173976193 hasRelatedWork W4300018864 @default.
- W173976193 isParatext "false" @default.
- W173976193 isRetracted "false" @default.
- W173976193 magId "173976193" @default.
- W173976193 workType "article" @default.