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Elastic drifted Brownian motions and non-local boundary conditions

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  • D’Ovidio, Mirko
  • Iafrate, Francesco

Abstract

We provide a deep connection between elastic drifted Brownian motions and inverses to tempered subordinators. Based on this connection, we establish a link between multiplicative functionals and dynamical boundary conditions given in terms of non-local equations in time. Indeed, we show that the multiplicative functional associated to the elastic Brownian motion with drift is equivalent to a functional associated with non-local boundary conditions of tempered type. By exploiting such connections we write some functionals of the drifted Brownian motion in terms of a simple (positive and non-decreasing) process, the inverse of a tempered subordinator. In our view, such a representation is useful in many applications and brings new light on dynamic boundary value problems.

Suggested Citation

  • D’Ovidio, Mirko & Iafrate, Francesco, 2024. "Elastic drifted Brownian motions and non-local boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:spapps:v:167:y:2024:i:c:s0304414923002004
    DOI: 10.1016/j.spa.2023.104228
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    References listed on IDEAS

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    1. Fausto Ferrari, 2018. "Weyl and Marchaud Derivatives: A Forgotten History," Mathematics, MDPI, vol. 6(1), pages 1-25, January.
    2. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    3. Alvaro Cartea & Diego del-Castillo-Negrete, 2007. "On the Fluid Limit of the Continuous-Time Random Walk with General Lévy Jump Distribution Functions," Birkbeck Working Papers in Economics and Finance 0708, Birkbeck, Department of Economics, Mathematics & Statistics.
    4. Chen, Zhen-Qing, 2017. "Time fractional equations and probabilistic representation," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 168-174.
    5. Iafrate, F. & Orsingher, E., 2021. "On the sojourn time of a generalized Brownian meander," Statistics & Probability Letters, Elsevier, vol. 168(C).
    6. repec:dau:papers:123456789/1392 is not listed on IDEAS
    7. Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
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    Cited by:

    1. Francesco Iafrate & Costantino Ricciuti, 2024. "Some Families of Random Fields Related to Multiparameter Lévy Processes," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3055-3088, November.

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