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Drift criteria for persistence of discrete stochastic processes on the line with examples of application

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  • Giulio Bottazzi
  • Pietro Dindo

Abstract

We provide sufficient conditions for the persistence or transience of stochastic processes on the real line based on the behavior of the first and second moment of their conditional increments at the boundaries. Our findings extend previous results in the literature (Lamperti, 1960) to the large class of discrete-time processes with bounded increments. We present some examples of application in the domain of economics.

Suggested Citation

  • Giulio Bottazzi & Pietro Dindo, 2015. "Drift criteria for persistence of discrete stochastic processes on the line with examples of application," LEM Papers Series 2015/26, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    • Handle: RePEc:ssa:lemwps:2015/26
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    Cited by:

    1. Dindo, Pietro, 2019. "Survival in speculative markets," Journal of Economic Theory, Elsevier, vol. 181(C), pages 1-43.
    2. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2018. "Long-run heterogeneity in an exchange economy with fixed-mix traders," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 407-447, August.
    3. Daniele Giachini, 2018. "Rationality and Asset Prices under Belief Heterogeneity," LEM Papers Series 2018/07, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    4. Daniele Giachini, 2021. "Rationality and asset prices under belief heterogeneity," Journal of Evolutionary Economics, Springer, vol. 31(1), pages 207-233, January.
    5. Bottazzi, Giulio & Giachini, Daniele, 2017. "Wealth and price distribution by diffusive approximation in a repeated prediction market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 473-479.
    6. G. Bottazzi & D. Giachini, 2019. "Far from the madding crowd: collective wisdom in prediction markets," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1461-1471, September.
    7. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2019. "Momentum and reversal in financial markets with persistent heterogeneity," Annals of Finance, Springer, vol. 15(4), pages 455-487, December.
    8. Bottazzi, Giulio & Dindo, Pietro, 2022. "Drift criteria for persistence of discrete stochastic processes on the line," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    9. Giulio Bottazzi & Daniele Giachini, 2018. "New Results on Betting Strategies, Market Selection, and the Role of Luck," LEM Papers Series 2018/08, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.

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