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First exit time from a bounded interval for pseudo-processes driven by the equation ∂/∂t=(−1)N−1∂2N/∂x2N

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  • Lachal, Aimé

Abstract

Let N be an integer greater than 1. We consider the pseudo-process X=(Xt)t≥0 driven by the high-order heat-type equation ∂/∂t=(−1)N−1∂2N/∂x2N. Let us introduce the first exit time τab from a bounded interval (a,b) by X (a,b∈R) together with the related location, namely Xτab.

Suggested Citation

  • Lachal, Aimé, 2014. "First exit time from a bounded interval for pseudo-processes driven by the equation ∂/∂t=(−1)N−1∂2N/∂x2N," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1084-1111.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:2:p:1084-1111
    DOI: 10.1016/j.spa.2013.09.016
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    References listed on IDEAS

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    1. Hochberg, Kenneth J. & Orsingher, Enzo, 1994. "The arc-sine law and its analogs for processes governed by signed and complex measures," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 273-292, August.
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    3. Lachal, Aimé, 2008. "First hitting time and place for pseudo-processes driven by the equation subject to a linear drift," Stochastic Processes and their Applications, Elsevier, vol. 118(1), pages 1-27, January.
    4. Beghin, Luisa & Hochberg, Kenneth J. & Orsingher, Enzo, 2000. "Conditional maximal distributions of processes related to higher-order heat-type equations," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 209-223, February.
    5. Aimé Lachal, 2012. "A Survey on the Pseudo-process Driven by the High-order Heat-type Equation $\boldsymbol{\partial/\partial t=\pm\partial^N\!/\partial x^N}$ Concerning the Hitting and Sojourn Times," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 549-566, September.
    6. Beghin, L. & Orsingher, E., 2005. "The distribution of the local time for "pseudoprocesses" and its connection with fractional diffusion equations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 1017-1040, June.
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