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Raluca M. Balan - One of the best experts on this subject based on the ideXlab platform.

  • A Markov Property for Set-Indexed Processes
    Journal of Theoretical Probability, 2002
    Co-Authors: Raluca M. Balan, B. G. Ivanoff
    Abstract:

    We consider a type of Markov Property for set-indexed processes which is satisfied by all processes with independent increments and which allows us to introduce a transition system theory leading to the construction of the process. A set-indexed generator is defined such that it completely characterizes the distribution of the process.

  • A strong Markov Property for set-indexed processes
    Statistics & Probability Letters, 2001
    Co-Authors: Raluca M. Balan
    Abstract:

    We introduce adapted sets and optional sets and we study a type of strong Markov Property for set-indexed processes that can be associated with the sharp Markov Property defined by Ivanoff and Merzbach (Proceedings of the International Conference on Stochastic Models, June 1998, Carleton University, Can. Math. Soc. Conf. Proc. 26 (2000) 217).

Paul Balança - One of the best experts on this subject based on the ideXlab platform.

  • An Increment-Type Set-Indexed Markov Property
    Journal of Theoretical Probability, 2015
    Co-Authors: Paul Balança
    Abstract:

    We present and study a Markov Property, named $$\mathcal C$$ C  -Markov, adapted to processes indexed by a general collection of sets. This new definition fulfils one important expectation for a set-indexed Markov Property: there exists a natural generalization of the concept of transition operator which leads to characterization and construction theorems of  $$\mathcal C$$ C  -Markov processes. Several usual Markovian notions, including Feller and strong Markov properties, are also developed in this framework. Actually, the $$\mathcal C$$ C  - Markov Property turns out to be a natural extension of the two-parameter $$*$$ ∗ -Markov Property to the multiparameter and the set-indexed settings. Moreover, extending a classic result of the real-parameter Markov theory, sample paths of multiparameter $$\mathcal C$$ C  -Feller processes are proved to be almost surely right-continuous. Concepts and results presented in this study are illustrated with various examples.

  • An increment type set-indexed Markov Property
    arXiv: Probability, 2012
    Co-Authors: Paul Balança
    Abstract:

    In this article is introduced and studied a set-indexed Markov Property named C-Markov. This new definition fulfils one important expectation for a Markov Property: there exists a natural set-indexed generalization of the concept of transition operator which leads to characterization and construction theorems for C-Markov processes. Several other usual Markovian notions, including Feller and strong Markov properties, can also be developed in this framework. Actually, the C-Markov Property turns out to be a natural extension of the two-parameter \ast-Markov Property to the multiparameter and as well the set-indexed settings. Moreover, generalizing a classic result of the real-parameter Markov theory, sample paths of multiparameter C-Feller processes are proved to be almost surely right-continuous. Concepts and results introduced in this study are illustrated with various examples.

Christoph Mainberger - One of the best experts on this subject based on the ideXlab platform.

  • stability and Markov Property of forward backward minimal supersolutions
    Electronic Journal of Probability, 2016
    Co-Authors: Samuel Drapeau, Christoph Mainberger
    Abstract:

    We show stability and locality of the minimal supersolution of a forward backward stochastic differential equation with respect to the underlying forward process under weak assumptions on the generator. The forward process appears both in the generator and the terminal condition. Painleve-Kuratowski and Convex Epi-convergence are used to establish the stability. For Markovian forward processes the minimal supersolution is shown to have the Markov Property. Furthermore, it is related to a time-shifted problem and identified as a viscosity supersolution of a corresponding PDE.

  • Stability and Markov Property of Forward Backward Minimal Supersolutions
    arXiv: Probability, 2015
    Co-Authors: Samuel Drapeau, Christoph Mainberger
    Abstract:

    We show stability and locality of the minimal supersolution of a forward backward stochastic differential equation with respect to the underlying forward process under weak assumptions on the generator. The forward process appears both in the generator and the terminal condition. Painlev\'e-Kuratowski and Convex Epi-convergence are used to establish the stability. For Markovian forward processes the minimal supersolution is shown to have the Markov Property. Furthermore, it is related to a time-shifted problem and identified as the unique minimal viscosity supersolution of a corresponding PDE.

B. G. Ivanoff - One of the best experts on this subject based on the ideXlab platform.

  • A Markov Property for Set-Indexed Processes
    Journal of Theoretical Probability, 2002
    Co-Authors: Raluca M. Balan, B. G. Ivanoff
    Abstract:

    We consider a type of Markov Property for set-indexed processes which is satisfied by all processes with independent increments and which allows us to introduce a transition system theory leading to the construction of the process. A set-indexed generator is defined such that it completely characterizes the distribution of the process.

John B. Walsh - One of the best experts on this subject based on the ideXlab platform.