Displaying similar documents to “Transformation of Markov processes by multiplicative functionals”

Jumping Markov Processes

J. Jacod, A. V. Skorokhod (1996)

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

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Extending the Wong-Zakai theorem to reversible Markov processes

Richard F. Bass, B. Hambly, Terry Lyons (2002)

Journal of the European Mathematical Society

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We show how to construct a canonical choice of stochastic area for paths of reversible Markov processes satisfying a weak Hölder condition, and hence demonstrate that the sample paths of such processes are rough paths in the sense of Lyons. We further prove that certain polygonal approximations to these paths and their areas converge in p -variation norm. As a corollary of this result and standard properties of rough paths, we are able to provide a significant generalization of the classical...

Tangential Markov inequality in L p norms

Agnieszka Kowalska (2015)

Banach Center Publications

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In 1889 A. Markov proved that for every polynomial p in one variable the inequality | | p ' | | [ - 1 , 1 ] ≤ ( d e g p ) ² | | p | | [ - 1 , 1 ] is true. Moreover, the exponent 2 in this inequality is the best possible one. A tangential Markov inequality is a generalization of the Markov inequality to tangential derivatives of certain sets in higher-dimensional Euclidean spaces. We give some motivational examples of sets that admit the tangential Markov inequality with the sharp exponent. The main theorems show that the results on certain arcs...

Markov's property of the Cantor ternary set

Leokadia Białas, Alexander Volberg (1993)

Studia Mathematica

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We prove that the Cantor ternary set E satisfies the classical Markov inequality (see [Ma]): for each polynomial p of degree at most n (n = 0, 1, 2,...) (M) | p ' ( x ) | ≤ M n m s u p E | p | for x ∈ E, where M and m are positive constants depending only on E.

A note on Markov operators and transition systems

Bartosz Frej (2002)

Colloquium Mathematicae

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On a compact metric space X one defines a transition system to be a lower semicontinuous map X → 2 X . It is known that every Markov operator on C(X) induces a transition system on X and that commuting of Markov operators implies commuting of the induced transition systems. We show that even in finite spaces a pair of commuting transition systems may not be induced by commuting Markov operators. The existence of trajectories for a pair of transition systems or Markov operators is also investigated. ...

The scaling limits of a heavy tailed Markov renewal process

Julien Sohier (2013)

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

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In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the α -stable regenerative set. We then apply these results to the strip wetting model which is a random walk S constrained above a wall and rewarded or penalized when it hits the strip [ 0 , ∞ ) × [ 0 , a ] where a is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.

A two-disorder detection problem

Krzysztof Szajowski (1997)

Applicationes Mathematicae

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Suppose that the process X = { X n , n ∈ ℕ } is observed sequentially. There are two random moments of time θ 1 and θ 2 , independent of X, and X is a Markov process given θ 1 and θ 2 . The transition probabilities of X change for the first time at time θ 1 and for the second time at time θ 2 . Our objective is to find a strategy which immediately detects the distribution changes with maximal probability based on observation of X. The corresponding problem of double optimal stopping is constructed. The optimal strategy...