A New Formula for Some Linear Stochastic Equations with Applications
نویسندگان
چکیده
We give a representation of the solution for a stochastic linear equation of the form Xt = Yt+ ∫ (0,t] Xs−dZs where Z is a càdlàg semimartingale and Y is a càdlàg adapted process with bounded variation on finite intervals. As an application we study the case where Y and −Z are nondecreasing, jointly have stationary increments and the jumps of −Z are bounded by 1. Special cases of this process are shot-noise processes, growth collapse (additive increase, multiplicative decrease) processes and clearing processes. When Y and Z are in addition independent Lévy processes the resulting X is called a generalized Ornstein-Uhlenbeck process.
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