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Persistence probabilities for stationary increment processes

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  • Aurzada, Frank
  • Guillotin-Plantard, Nadine
  • Pène, Françoise

Abstract

We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion; random walks in random sceneries; random processes in Brownian scenery; and the Matheron–de Marsily model in Z2 with random orientations of the horizontal layers. Using a new approach, strongly related to the study of the range, we obtain an upper bound of the optimal order in general and improved lower bounds (compared to previous literature) for many specific processes.

Suggested Citation

  • Aurzada, Frank & Guillotin-Plantard, Nadine & Pène, Françoise, 2018. "Persistence probabilities for stationary increment processes," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1750-1771.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:5:p:1750-1771
    DOI: 10.1016/j.spa.2017.07.016
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    References listed on IDEAS

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    1. Redner, S., 1990. "Superdiffusion in random velocity fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 551-560.
    2. Guillotin-Plantard, Nadine & Poisat, Julien, 2013. "Quenched central limit theorems for random walks in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1348-1367.
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    Cited by:

    1. Aurzada, Frank & Mukherjee, Sumit, 2023. "Persistence probabilities of weighted sums of stationary Gaussian sequences," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 286-319.
    2. Peng, Qidi & Rao, Nan, 2023. "Fractional Brownian motion: Small increments and first exit time from one-sided barrier," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. Aurzada, Frank & Buck, Micha & Kilian, Martin, 2020. "Penalizing fractional Brownian motion for being negative," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6625-6637.
    4. Christian Mönch, 2022. "Universality for Persistence Exponents of Local Times of Self-Similar Processes with Stationary Increments," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1842-1862, September.

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