Generalized Ornstein-Uhlenbeck processes
نویسندگان
چکیده
منابع مشابه
Multivariate Generalized Ornstein-Uhlenbeck Processes
De Haan and Karandikar [12] introduced generalized Ornstein–Uhlenbeck processes as one-dimensional processes (Vt)t≥0 which are basically characterized by the fact that for each h > 0 the equidistantly sampled process (Vnh)n∈N0 satisfies the random recurrence equation Vnh = A(n−1)h,nhV(n−1)h + B(n−1)h,nh, n ∈ N, where (A(n−1)h,nh, B(n−1)h,nh)n∈N is an i.i.d. sequence with positive A0,h for each ...
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We introduce an extended version of the fractional Ornstein-Uhlenbeck (FOU) process where the integrand is replaced by the exponential of an independent Lévy process. We call the process the generalized fractional Ornstein-Uhlenbeck (GFOU) process. Alternatively, the process can be constructed from a generalized Ornstein-Uhlenbeck (GOU) process using an independent fractional Brownian motion (F...
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The generalized Ornstein-Uhlenbeck process Vt = e −ξt ( V0 + ∫ t 0 edηs ) , t ≥ 0, driven by a bivariate Lévy process (ξt, ηt)t≥0 with starting random variable V0 independent of (ξ, η) fulfills the stochastic differential equation dVt = Vt−dUt + dLt for another bivariate Lévy process (Ut, Lt)t≥0, which is determined completely by (ξ, η). In particular it holds ξt = − log(E(U)t), t ≥ 0, where E(...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2006
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2206878