Densities for Ornstein-Uhlenbeck processes with jumps
نویسندگان
چکیده
منابع مشابه
2 00 8 Densities for Ornstein - Uhlenbeck processes with jumps 11 april 2008
Abstract: We consider an Ornstein-Uhlenbeck process with values in Rn driven by a Lévy process (Zt) taking values in R d with d possibly smaller than n. The Lévy noise can have a degenerate or even vanishing Gaussian component. Under a controllability rank condition and a mild assumption on the Lévy measure of (Zt), we prove that the law of the Ornstein-Uhlenbeck process at any time t > 0 has a...
متن کاملA ug 2 00 7 Densities for Ornstein - Uhlenbeck processes with jumps 8 august 2007
Abstract: We consider an Ornstein-Uhlenbeck process with values in Rn driven by a Lévy process (Zt) taking values in R d with d possibly smaller than n. The Lévy noise can have a degenerate or even vanishing Gaussian component. Under a controllability condition and an assumption on the Lévy measure of (Zt), we prove that the law of the Ornstein-Uhlenbeck process at any time t > 0 has a density ...
متن کاملMultivariate 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 ...
متن کاملMarkov-modulated Ornstein-Uhlenbeck processes
In this paper we consider an Ornstein-Uhlenbeck (ou) process (M(t))t>0 whose parameters are determined by an external Markov process (X(t))t>0 on a nite state space {1, . . . , d}; this process is usually referred to as Markov-modulated Ornstein-Uhlenbeck (or: mmou). We use stochastic integration theory to determine explicit expressions for the mean and variance of M(t). Then we establish a sys...
متن کاملGeneralized fractional Ornstein-Uhlenbeck processes
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2008
ISSN: 0024-6093
DOI: 10.1112/blms/bdn099