Predictive sets

2020 ◽  
pp. 2140006
Author(s):  
Nishant Chandgotia ◽  
Benjamin Weiss
Keyword(s):  
Harmonic Analysis ◽  
Gaussian Processes ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Zero Entropy

A set [Formula: see text] is called predictive if for any zero entropy finite-valued stationary process [Formula: see text], [Formula: see text] is measurable with respect to [Formula: see text]. We know that [Formula: see text] is a predictive set. In this paper, we give sufficient conditions and necessary ones for a set to be predictive. We also discuss linear predictivity, predictivity among Gaussian processes and relate these to Riesz sets which arise in harmonic analysis.

scholarly journals Algebraic entropies, Hopficity and co-Hopficity of direct sums of Abelian Groups

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Brendan Goldsmith ◽  
Ketao Gong
Keyword(s):  
Abelian Groups ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Direct Sums ◽  
Direct Sum ◽  
Zero Entropy ◽  
Necessary And Sufficient

AbstractNecessary and sufficient conditions to ensure that the direct sum of two Abelian groups with zero entropy is again of zero entropy are still unknown; interestingly the same problem is also unresolved for direct sums of Hopfian and co-Hopfian groups.We obtain sufficient conditions in some situations by placing restrictions on the homomorphisms between the groups. There are clear similarities between the various cases but there is not a simple duality involved.

The stochastic equation Yt+1 = AtYt + Bt with non-stationary coefficients

2001 ◽  
Vol 38 (1) ◽  
pp. 80-94 ◽  
Author(s):  
Ulrich Horst
Keyword(s):  
Global Convergence ◽  
Random Environment ◽  
Linear Relation ◽  
Stochastic Equation ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Convergence Result ◽  
Stationary Case ◽  
Finite Dimensional ◽  
Long Run

In this paper, we consider the stochastic sequence {Yt}t∊ℕ defined recursively by the linear relation Yt+1 = AtYt + Bt in a random environment which is described by the non-stationary process {(At, Bt)}t∊ℕ. We formulate sufficient conditions on the environment which ensure that the finite-dimensional distributions of {Yt}t∊ℕ converge weakly to the finite-dimensional distributions of a unique stationary process. If the driving sequence {(At, Bt)}t∊ℕ becomes stationary in the long run, then we can establish a global convergence result. This extends results of Brandt (1986) and Borovkov (1998) from the stationary to the non-stationary case.

Further results on ASTA for general stationary processes and related problems

1990 ◽  
Vol 27 (4) ◽  
pp. 792-804 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Ronald W. Wolff
Keyword(s):  
Point Process ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Jump Process ◽  
Arrival Process ◽  
General Process ◽  
Left Hand ◽  
Time Averages ◽  
Semi Markov Processes ◽  
Necessary And Sufficient

We consider the equivalence of state probabilities of a general stationary process at an arbitrary time and at embedded epochs of a given point process, which is called ASTA (Arrivals See Time Averages). By using an event-conditonal intensity, we give necessary and sufficient conditions for ASTA for a large class of state sets, which determines a state distribution. We do not need any additional assumptions except that the general process has left-hand limits at all points of time. Especially, for a stationary pure-jump process with a point process, ASTA is obtained for all state sets. As an application of those results, Anti-PASTA is obtained for a pure-jump Markov process and a certain class of GSMP (Generalized Semi-Markov Processes), where Anti-PASTA means that ASTA implies that the arrival process is Poisson.

scholarly journals On a Necessary Condition for the Sample Path Continuity of Weakly Stationary Processes

1970 ◽  
Vol 38 ◽  
pp. 103-111 ◽  
Author(s):  
Izumi Kubo
Keyword(s):  
Distribution Function ◽  
Asymptotic Behavior ◽  
Spectral Distribution ◽  
Covariance Function ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Sample Path ◽  
Necessary Condition ◽  
Stationary Processes ◽  
Spectral Distribution Function

We shall discuss the sample path continuity of a stationary process assuming that the spectral distribution function F(λ) is given. Many kinds of sufficient conditions have been given in terms of the covariance function or the asymptotic behavior of the spectral distribution function.

On the Lamperti transform of the fractional Brownian sheet

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Marwa Khalil ◽  
Ciprian Tudor ◽  
Mounir Zili
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Gaussian Processes ◽  
Stationary Process ◽  
Similar Process ◽  
Brownian Sheet ◽  
Fractional Brownian Sheet ◽  
Self Similar ◽  
Strictly Stationary Process

AbstractIn 1962 Lamperti introduced a transformation that associates to every non-trivial self-similar process a strictly stationary process. This transform has been widely studied for Gaussian processes and in particular for fractional Brownian motion. Our aim is to analyze various properties of the Lamperti transform of the fractional Brownian sheet. We give the stochastic differential equation satisfied by this transform and we represent it as a series of independent Ornstein-Uhlenbeck sheets.

scholarly journals Backward Coalescence Times for Perfect Simulation of Chains with Infinite Memory

2012 ◽  
Vol 49 (02) ◽  
pp. 319-337 ◽  
Author(s):  
Emilio De Santis ◽  
Mauro Piccioni
Keyword(s):  
Stationary Process ◽  
Past History ◽  
A Priori ◽  
Sufficient Conditions ◽  
Perfect Simulation ◽  
Simulation Algorithm ◽  
Infinite Memory ◽  
Countable State ◽  
Weaker Conditions ◽  
Coalescence Times

This paper is devoted to the perfect simulation of a stationary process with an at most countable state space. The process is specified through a kernel, prescribing the probability of the next state conditional to the whole past history. We follow the seminal work of Comets, Fernández and Ferrari (2002), who gave sufficient conditions for the construction of a perfect simulation algorithm. We define backward coalescence times for these kind of processes, which allow us to construct perfect simulation algorithms under weaker conditions than in Comets, Fernández and Ferrari (2002). We discuss how to construct backward coalescence times (i) by means of information depths, taking into account some a priori knowledge about the histories that occur; and (ii) by identifying suitable coalescing events.

Sign in / Sign up

Export Citation Format

Share Document