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Variational formulas for the exit time of Hunt processes generated by semi-Dirichlet forms

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  • Huang, Lu-Jing
  • Kim, Kyung-Youn
  • Mao, Yong-Hua
  • Wang, Tao

Abstract

Variational formulas for the Laplace transform of the exit time from an open set of a Hunt process generated by a regular lower bounded semi-Dirichlet form are established. While for symmetric Markov processes, variational formulas are derived for the exponential moments of the exit time. As applications, we provide some comparison theorems and quantitative relations of the exponential moments and Poincaré inequalities.

Suggested Citation

  • Huang, Lu-Jing & Kim, Kyung-Youn & Mao, Yong-Hua & Wang, Tao, 2022. "Variational formulas for the exit time of Hunt processes generated by semi-Dirichlet forms," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 380-399.
    • Handle: RePEc:eee:spapps:v:148:y:2022:i:c:p:380-399
    DOI: 10.1016/j.spa.2022.03.005
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    References listed on IDEAS

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    1. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    2. Ditlevsen, Susanne, 2007. "A result on the first-passage time of an Ornstein-Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1744-1749, December.
    3. Mijatović, Aleksandar & Pistorius, Martijn R., 2012. "On the drawdown of completely asymmetric Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3812-3836.
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    1. Huang, Lu-Jing & Wang, Tao, 2023. "Dirichlet eigenvalues and exit time moments for symmetric Markov processes," Statistics & Probability Letters, Elsevier, vol. 193(C).

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