Stationary solutions of the stochastic differential equation dVt = Vt-dUt + Lt with Levy noise

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Behme, Anita¹  Lindner, Alexander¹  Maller, Ross^2,3 

[1] Tech Univ Carolo Wilhelmina Braunschweig, Inst Math Stochast, D-38106 Braunschweig, Germany

[2] Australian Natl Univ, Ctr Math Anal, Canberra, ACT, Australia

[3] Australian Natl Univ, Sch Finance & Appl Stat, Canberra, ACT, Australia

关键词: Stochastic differential equation;    Levy process;    Generalized;    Ornstein-Uhlenbeck process;    Stochastic exponential;    Stationarity;    Non causal;    Filtration expansion;   

DOI  :  10.1016/j.spa.2010.09.003

来源: Elsevier

【 摘 要 】

For a given bivariate Levy process (U-t L-t)(t >= 0) necessary and sufficient conditions for the existence of a strictly stationary solution of the stochastic differential equation dV(t) = dU(t) + dL(t) are obtained Neither strict positivity of the stochastic exponential of U nor independence of V-0 and (U L) is assumed and non-causal solutions may appear The form of the stationary solution is determined and shown to be unique in distribution, provided it exists For non causal solutions a sufficient condition for U and L to remain semimartingales with respect to the corresponding expanded filtration is given (c) 2010 Elsevier B V All rights reserved

【 授权许可】

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