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  • 60J30  (1)
  • Arc-sine law  (1)
  • Inviscid Burgers equation  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Some independence results related to the arc-sine law (1996)
    Springer
    Journal of theoretical probability 9 (1996), S. 447-458 
    Details
    ISSN: 1572-9230
    Keywords: Arc-sine law ; Lévy process ; local time
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We provide proofs for recent results of Getoor and Sharpe on the distribution of local times on rays for certain planar Lévy processes which were invalidated by an appeal to an incorrect assertion. Our arguments rely on independence properties related to the arc-sine law.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02214659
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  • 2
    Electronic Resource
    Electronic Resource
    Regenerative embedding of Markov sets (1997)
    Springer
    Probability theory and related fields 108 (1997), S. 559-571 
    Details
    ISSN: 1432-2064
    Keywords: Key words: Markov set ; Regenerative property ; Skorohod embedding ; Subordinator. ; Mathematics Subject Classification (1991): 60D05 ; 60J30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary.  Given a closed Markov (i.e. regenerative) set in [0,∞), we characterize the laws of the Markov sets which are regeneratively embedded into the latter. Typically, let Φ(1) and Φ(2) be two Laplace exponents corresponding to two regenerative laws, and M (2) a Markov set with exponent Φ(2). There exists a Markov set M (1) with exponent Φ(1) which is regeneratively embedded into M (2) if and only if Φ(1)/Φ(2) is a completely monotone function. Several examples and applications are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004400050121
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  • 3
    Electronic Resource
    Electronic Resource
    Large-Deviations Estimates in Burgers Turbulence with Stable Noise Initial Data (1998)
    Springer
    Journal of statistical physics 91 (1998), S. 655-667 
    Details
    ISSN: 1572-9613
    Keywords: Inviscid Burgers equation ; random initial velocity ; large deviations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider the inviscid Burgers equation where the initial datum is given by a stable (Lévy) noise. The asymptotic behavior of the tail distribution of the solution is described; the decay is much faster in the case when the stable noise is completely skewed to the left.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023081728243
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