ANALYTIC PROOF OF PECHERSKII-ROGOZIN IDENTITY AND WIENER-HOPF FACTORIZATION

作者：Kuznetsov A^*

来源：Theory of Probability and Its Applications, 2011, 55(3): 432-443.

DOI：10.1137/S0040585X97984929

• Levy process
• Wiener-Hopf factorization
• Pecherskii-Rogozin identity
• integral equation
• Riemann boundary value problem
• Sokhotsky's formulas

We present an analytic proof of the Pecherskii-Rogozin identity and the Wiener-Hopf factorization. The proof is rather general and requires only one mild restriction on the tail of the Levy measure. The starting point of the proof of the Pecherskii-Rogozin identity is a two-dimensional integral equation satisfied by the joint distribution of the first passage time and the overshoot. This equation is reduced to a one-dimensional Wiener-Hopf integral equation, which is then solved using classical techniques from the theory of the Riemann boundary value problems. The Wiener-Hopf factorization is then derived as a corollary of the Pecherskii-Rogozin identity.

• 出版日期2011