Recurrence conditions for multidimensional processes of Ornstein-Uhlenbeck type
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Abstract:
A stochastic process of Ornstein-Uhlenbeck type on the Euclidean space is a Markov process obtained from a spatially homogeneous Markov process undergoing a linear drift force determined by a matrix -Q. We give a criterion of recurrence and transience for a process of this type under the assumption that Q is diagonalizable and its eigenvalues are positive. No restriction is imposed on the part of the spatially homogeneous Markov process. Rigorous definition of our process is as follows. Let G be an operator defined byread more
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References
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Journal ArticleDOI
Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type
Ken-iti Sato,Makoto Yamazato +1 more
TL;DR: In this article, the class of limit distributions of Ornstein-Uhlenbeck processes on R d is characterized, and integro-differential equations for operator-self-decomposable distributions are established.
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On a continuous analogue of the stochastic difference equation Xn=ρXn-1+Bn
TL;DR: The main analytical tool used to obtain these results is a theorem of Lukacs concerning characteristic functions of certain stochastic integrals as mentioned in this paper, and several other related results are obtained.
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An integral representation for selfdecomposable banach space valued random variables
Zbigniew J. Jurek,Wim Vervaat +1 more
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Langevins stochastic differential equation extended by a time-delayed term
Uwe Küchler,Beatrice Mensch +1 more
TL;DR: The stochastic differential equation is a generalization of Langevin's equation as discussed by the authors, which is obtained if b = 0. Necessary and sufficient conditions on a, b and r are given under which a stationary so...
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