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Sticky Brownian motion as the strong limit of a sequence of random walks

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  • Amir, Madjid

Abstract

We provide here a constructive definition of the sticky Brownian motion as we show that it is the almost sure uniform limit of path functions of a time changed random walk. The transition distribution of this process is also derived.

Suggested Citation

  • Amir, Madjid, 1991. "Sticky Brownian motion as the strong limit of a sequence of random walks," Stochastic Processes and their Applications, Elsevier, vol. 39(2), pages 221-237, December.
    • Handle: RePEc:eee:spapps:v:39:y:1991:i:2:p:221-237
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    Cited by:

    1. Hongshuai Dai, 2022. "Tandem fluid queue with long-range dependent inputs: sticky behaviour and heavy traffic approximation," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 165-196, June.
    2. Christian Meier & Lingfei Li & Gongqiu Zhang, 2019. "Markov Chain Approximation of One-Dimensional Sticky Diffusions," Papers 1910.14282, arXiv.org.
    3. Amir, Madjid & Knight, Frank B., 1995. "Law of the iterated logarithm and local variations at zero of the sticky Brownian motion," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 289-295, May.
    4. Alexis Anagnostakis, 2023. "Pricing and hedging for a sticky diffusion," Papers 2311.17011, arXiv.org, revised Oct 2024.
    5. Hirotaka Fushiya, 2010. "Weak Convergence Theorem of a Nonnegative Random Walk to Sticky Reflected Brownian Motion," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1157-1181, December.

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