On a Comparison Result for Markov Processes

Rüschendorf, Ludger

doi:10.1017/s0021900200004125

Cited by 5 publications

(10 citation statements)

References 18 publications

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“…Szekli (1995) and Rüschendorf (2008) extended this result to more general state spaces [29,Ch.3.7], [23,Cor.3.1]. Rüschendorf also extended the Liggett condition for PSA of the Markov process [23,Cor.3.4].…”

Section: Introductionmentioning

confidence: 91%

“…For time-inhomogeneous Markov processes X and Y , with Markov evolutions (S s,t ) s≤t and (T s,t ) s≤t , we say Y dominates X with respect to F if S s,t f ≤ T s,t f for all s ≤ t and all f ∈ F. Rüschendorf has proven comparison theorems for general Markov processes which are time-homogeneous (2008) [17] and time-inhomogeneous (2016) [18]. These sufficient conditions were based on the generators of the Markov process.…”

Section: Comparison Of Markov Processesmentioning

confidence: 99%

“…Observe that for all f ∈ For more on comparison theorems of Markov processes, see Rüschendorf [17,18].…”

Section: Comparison Of Markov Processesmentioning

confidence: 99%

“…Liggett (1985) proved a necessary and sufficient condition for association of stochastically monotone Markov processes on compact state spaces based on the generator of the process [18]. Szekli (1995) and Rüschendorf (2008) extended this result to more general state spaces [29,Ch.3.7], [23,Cor.3.1]. Rüschendorf also extended the Liggett condition for PSA of the Markov process [23,Cor.3.4].…”

Section: Introductionmentioning

confidence: 98%

See 3 more Smart Citations

On association and other forms of positive dependence for Feller processes

2019

J. Appl. Probab.

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We characterize various forms of positive dependence, such as association, positive supermodular association and dependence, and positive orthant dependence, for jump-Feller processes. Such jump processes can be studied through their statespace dependent Lévy measures. It is through these Lévy measures where we will provide our characterization. Finally, we present applications of these results to stochastically monotone Feller processes, including Lévy processes, the Ornstein-Uhlenbeck process, pseudo-Poisson processes, and subordinated Feller processes.

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Section: Introductionmentioning

confidence: 91%

Section: Comparison Of Markov Processesmentioning

confidence: 99%

“…Observe that for all f ∈ For more on comparison theorems of Markov processes, see Rüschendorf [17,18].…”

Section: Comparison Of Markov Processesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

On association and other forms of positive dependence for Feller processes

2019

J. Appl. Probab.

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“…Stochastic ordering and comparison results for Markov processes are a basic problem of probability theory. They have a long history and are motivated by a number of applications in a variety of fields (see Massey (1987), Cox et al (1996), Daduna and Szekli (2006), Rüschendorf (2008), Krasin and Melnikov (2009), Rüschendorf and Wolf (2011), Rüschendorf et al (2016), Criens (2017) and Criens (2019)). Various approaches ranging from analytic to coupling methods have been developed to this aim sometimes in the context of specific models or specific applications.…”

Section: Evolution Systems and Comparison Of Markov Processesmentioning

confidence: 99%

Comparison of Markov processes by the martingale comparison method

Köpfer¹,

Rüschendorf²

2019

Preprint

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Comparison results for Markov processes w.r.t. function class induced (integral) stochastic orders have a long history. The most general results so far for this problem have been obtained based on the theory of evolution systems on Banach spaces. In this paper we transfer the martingale comparison method, known for the comparison of semimartingales to Markovian semimartingales, to general Markov processes. The basic step of this martingale approach is the derivation of the supermartingale property of the linking process, giving a link between the processes to be compared. In this paper this property is achieved using in an essential way the characterization of Markov processes by the martingale problem. As a result the martingale comparison method gives a comparison result for Markov processes under a general alternative set of regularity conditions compared to the evolution system approach.

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Comparison of time-inhomogeneous Markov processes

Rüschendorf

Schnurr²,

Wolf

2016

Adv. Appl. Probab.

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Comparison results are given for time-inhomogeneous Markov processes with respect to function classes induced stochastic orderings. The main result states comparison of two processes, provided that the comparability of their infinitesimal generators as well as an invariance property of one process is assumed. The corresponding proof is based on a representation result for the solutions of inhomogeneous evolution problems in Banach spaces, which extends previously known results from the literature. Based on this representation, an ordering result for Markov processes induced by bounded and unbounded function classes is established. We give various applications to time-inhomogeneous diffusions, to processes with independent increments and to Lévy driven diffusion processes.

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On a Comparison Result for Markov Processes

Cited by 5 publications

References 18 publications

On association and other forms of positive dependence for Feller processes

On association and other forms of positive dependence for Feller processes

Comparison of Markov processes by the martingale comparison method

Comparison of time-inhomogeneous Markov processes

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