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Almost Sure Comparisons for First Passage Times of Diffusion Processes through Boundaries

Author

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  • L. Sacerdote

    (Università di Torino)

  • C. E. Smith

    (North Carolina State University)

Abstract

Conditions on the boundary and parameters that produce ordering in the first passage time distributions of two different diffusion processes are proved making use of comparison theorems for stochastic differential equations. Three applications of interest in stochastic modeling are presented: a sensitivity analysis for diffusion models characterized by means of first passage times, the comparison of different diffusion models where first passage times represent an important feature and the determination of upper and lower bounds for first passage time distributions.

Suggested Citation

  • L. Sacerdote & C. E. Smith, 2004. "Almost Sure Comparisons for First Passage Times of Diffusion Processes through Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 6(3), pages 323-341, September.
    • Handle: RePEc:spr:metcap:v:6:y:2004:i:3:d:10.1023_b:mcap.0000026563.27820.ff
    DOI: 10.1023/B:MCAP.0000026563.27820.ff
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    References listed on IDEAS

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    1. Di Crescenzo, Antonio & Ricciardi, Luigi M., 1996. "Comparing first-passage times for semi-Markov skip-free processes," Statistics & Probability Letters, Elsevier, vol. 30(3), pages 247-256, October.
    2. Maria Teresa Giraudo & Laura Sacerdote & Cristina Zucca, 2001. "A Monte Carlo Method for the Simulation of First Passage Times of Diffusion Processes," Methodology and Computing in Applied Probability, Springer, vol. 3(2), pages 215-231, June.
    3. Li, Haijun & Shaked, Moshe, 1995. "On the first passage times for Markov processes with monotone convex transition kernels," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 205-216, August.
    4. Ball, Clifford A. & Roma, Antonio, 1993. "A jump diffusion model for the European monetary system," Journal of International Money and Finance, Elsevier, vol. 12(5), pages 475-492, October.
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