Displaying similar documents to “Insensitivity analysis of Markov chains”

On the central limit theorem for some birth and death processes

Tymoteusz Chojecki (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Suppose that { X n : n 0 } is a stationary Markov chain and V is a certain function on a phase space of the chain, called an observable. We say that the observable satisfies the central limit theorem (CLT) if Y n : = N - 1 / 2 n = 0 N V ( X n ) converge in law to a normal random variable, as N + . For a stationary Markov chain with the L 2 spectral gap the theorem holds for all V such that V ( X 0 ) is centered and square integrable, see Gordin [7]. The purpose of this article is to characterize a family of observables V for which the CLT holds...

Evaluating default priors with a generalization of Eaton’s Markov chain

Brian P. Shea, Galin L. Jones (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We consider evaluating improper priors in a formal Bayes setting according to the consequences of their use. Let 𝛷 be a class of functions on the parameter space and consider estimating elements of 𝛷 under quadratic loss. If the formal Bayes estimator of every function in 𝛷 is admissible, then the prior is strongly admissible with respect to 𝛷 . Eaton’s method for establishing strong admissibility is based on studying the stability properties of a particular Markov chain associated with...

Copies of l p n ’s uniformly in the spaces Π 2 ( C [ 0 , 1 ] , X ) and Π 1 ( C [ 0 , 1 ] , X )

Dumitru Popa (2017)

Czechoslovak Mathematical Journal

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We study the presence of copies of l p n ’s uniformly in the spaces Π 2 ( C [ 0 , 1 ] , X ) and Π 1 ( C [ 0 , 1 ] , X ) . By using Dvoretzky’s theorem we deduce that if X is an infinite-dimensional Banach space, then Π 2 ( C [ 0 , 1 ] , X ) contains λ 2 -uniformly copies of l n ’s and Π 1 ( C [ 0 , 1 ] , X ) contains λ -uniformly copies of l 2 n ’s for all λ > 1 . As an application, we show that if X is an infinite-dimensional Banach space then the spaces Π 2 ( C [ 0 , 1 ] , X ) and Π 1 ( C [ 0 , 1 ] , X ) are distinct, extending the well-known result that the spaces Π 2 ( C [ 0 , 1 ] , X ) and 𝒩 ( C [ 0 , 1 ] , X ) are distinct.

Covariance structure of wide-sense Markov processes of order k ≥ 1

Arkadiusz Kasprzyk, Władysław Szczotka (2006)

Applicationes Mathematicae

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A notion of a wide-sense Markov process X t of order k ≥ 1, X t W M ( k ) , is introduced as a direct generalization of Doob’s notion of wide-sense Markov process (of order k=1 in our terminology). A base for investigation of the covariance structure of X t is the k-dimensional process x t = ( X t - k + 1 , . . . , X t ) . The covariance structure of X t W M ( k ) is considered in the general case and in the periodic case. In the general case it is shown that X t W M ( k ) iff x t is a k-dimensional WM(1) process and iff the covariance function of x t has the triangular...

Simplices rarely contain their circumcenter in high dimensions

Jon Eivind Vatne (2017)

Applications of Mathematics

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Acute triangles are defined by having all angles less than π / 2 , and are characterized as the triangles containing their circumcenter in the interior. For simplices of dimension n 3 , acuteness is defined by demanding that all dihedral angles between ( n - 1 ) -dimensional faces are smaller than π / 2 . However, there are, in a practical sense, too few acute simplices in general. This is unfortunate, since the acuteness property provides good qualitative features for finite element methods. The property...

H 2 convergence of solutions of a biharmonic problem on a truncated convex sector near the angle π

Abdelkader Tami, Mounir Tlemcani (2021)

Applications of Mathematics

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We consider a biharmonic problem Δ 2 u ω = f ω with Navier type boundary conditions u ω = Δ u ω = 0 , on a family of truncated sectors Ω ω in 2 of radius r , 0 < r < 1 and opening angle ω , ω ( 2 π / 3 , π ] when ω is close to π . The family of right-hand sides ( f ω ) ω ( 2 π / 3 , π ] is assumed to depend smoothly on ω in L 2 ( Ω ω ) . The main result is that u ω converges to u π when ω π with respect to the H 2 -norm. We can also show that the H 2 -topology is optimal for such a convergence result.

Probabilistic properties of a Markov-switching periodic G A R C H process

Billel Aliat, Fayçal Hamdi (2019)

Kybernetika

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In this paper, we propose an extension of a periodic G A R C H ( P G A R C H ) model to a Markov-switching periodic G A R C H ( M S - P G A R C H ), and provide some probabilistic properties of this class of models. In particular, we address the question of strictly periodically and of weakly periodically stationary solutions. We establish necessary and sufficient conditions ensuring the existence of higher order moments. We further provide closed-form expressions for calculating the even-order moments as well...

A note on the Π -property of some subgroups of finite groups

Zhengtian Qiu, Guiyun Chen, Jianjun Liu (2024)

Czechoslovak Mathematical Journal

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Let H be a subgroup of a finite group G . We say that H satisfies the Π -property in G if for any chief factor L / K of G , | G / K : N G / K ( H K / K L / K ) | is a π ( H K / K L / K ) -number. We obtain some criteria for the p -supersolubility or p -nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the Π -property.

Time-varying Markov decision processes with state-action-dependent discount factors and unbounded costs

Beatris A. Escobedo-Trujillo, Carmen G. Higuera-Chan (2019)

Kybernetika

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In this paper we are concerned with a class of time-varying discounted Markov decision models n with unbounded costs c n and state-action dependent discount factors. Specifically we study controlled systems whose state process evolves according to the equation x n + 1 = G n ( x n , a n , ξ n ) , n = 0 , 1 , ... , with state-action dependent discount factors of the form α n ( x n , a n ) , where a n and ξ n are the control and the random disturbance at time n , respectively. Assuming that the sequences of functions { α n } , { c n } and { G n } converge, in certain sense, to α ,...

Smoothness of Green's functions and Markov-type inequalities

Leokadia Białas-Cież (2011)

Banach Center Publications

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Let E be a compact set in the complex plane, g E be the Green function of the unbounded component of E with pole at infinity and M ( E ) = s u p ( | | P ' | | E ) / ( | | P | | E ) where the supremum is taken over all polynomials P | E 0 of degree at most n, and | | f | | E = s u p | f ( z ) | : z E . The paper deals with recent results concerning a connection between the smoothness of g E (existence, continuity, Hölder or Lipschitz continuity) and the growth of the sequence M ( E ) n = 1 , 2 , . . . . Some additional conditions are given for special classes of sets.

Soft local times and decoupling of random interlacements

Serguei Popov, Augusto Teixeira (2015)

Journal of the European Mathematical Society

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In this paper we establish a decoupling feature of the random interlacement process u d at level u , d 3 . Roughly speaking, we show that observations of u restricted to two disjoint subsets A 1 and A 2 of d are approximately independent, once we add a sprinkling to the process u by slightly increasing the parameter u . Our results differ from previous ones in that we allow the mutual distance between the sets A 1 and A 2 to be much smaller than their diameters. We then provide an important application...

On Π -property of some maximal subgroups of Sylow subgroups of finite groups

Zhengtian Qiu, Jianjun Liu, Guiyun Chen (2023)

Czechoslovak Mathematical Journal

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Let H be a subgroup of a finite group G . We say that H satisfies the Π -property in G if for any chief factor L / K of G , | G / K : N G / K ( H K / K L / K ) | is a π ( H K / K L / K ) -number. We study the influence of some p -subgroups of G satisfying the Π -property on the structure of G , and generalize some known results.