Adaptive estimation for affine stochastic delay differential equations

Markus Reiß

No 2003,18, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: Stochastic delay differential equations (SDDEs for short) appear naturally in the description of many processes, e.g. in population dynamics with a time lag due to an age-dependent birth rate (Scheutzow 1981), in economics where a certain "time to build" is needed (Kydland and Prescott 1982) or in laser technology (Garcia-Ojalvo and Roy 1996), in finance (Hobson and Rogers 1998) and in many engineering applications, see Kohmanovskii and Myshkis (1992) for an overview. They are also obtained as continuous-time limits of time series models, e.g. Jeantheau (2001), Reiß (2001). Among the huge variety of types of equations, the so-called affine stochastic delay differential equations form the fundamental class. They generalize the Langevin equation leading to the Ornstein-Uhlenbeck process and appear as continuous-time limits of linear autoregressive schemes.

Date: 2003
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