Joint distributions of the maximum and the process for higher-order diffusions

L. Beghin, E. Orsingher and T. Ragozina

Stochastic Processes and their Applications, 2001, vol. 94, issue 1, 71-93

Abstract: For processes X(t),t>0 governed by signed measures whose density is the fundamental solution of third and fourth-order heat-type equations (higher-order diffusions) the explicit form of the joint distribution of (max0[less-than-or-equals, slant]s[less-than-or-equals, slant]t X(s),X(t)) is derived. The expressions presented include all results obtained so far and, for the third-order case, prove to be genuine probability distributions. The case of more general fourth-order equations is also investigated and the distribution of the maximum is derived.

Keywords: Maximal; distributions; Feynman-Kac; functional; Higher-order; heat-type; equations; Signed; measures; Laplace; transforms; Airy; functions; Stable; laws; Fractional; integration (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (5)

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