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Relativistic Ornstein–Uhlenbeck Process

Journal of Statistical Physics, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Debbasch, F., Mallick, K., Rivet, J. P.
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The generalized Ornstein - Uhlenbeck process

Journal of Physics A: Mathematical and General, 1997
Summary: Langevin-like equations have been studied in the presence of arbitrary noise. The characteristic functional of the generalized Langevin process has been built up. Exact results for all cumulants are given. Particular stress has been put on the Campbell, dichotomous and radioactive decay noises.
Cáceres, Manuel O., Budini, Adrián A.
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Hyperbolic Ornstein–Uhlenbeck Process

Journal of Mathematical Sciences, 2016
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Critical Ornstein-Uhlenbeck processes

Applied Mathematics & Optimization, 1986
The Ornstein-Uhlenbeck position process with the invariant measure is shown to satisfy a variational principle quite analogous to Hamilton's least action principle of classical mechanics. To prove this, a stochastic calculus of variations is developed for processes with differentiable sample paths, and which form a diffusion together with their ...
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Superposition of Ornstein--Uhlenbeck Type Processes

Theory of Probability & Its Applications, 2001
This paper studies a class of superpositions of Ornstein-Uhlenbeck type processes in terms of integrals with respect to independently scattered random measures. The paper develops flexible classes of processes that incorporate long-range dependence and self-similarity-like properties and that are capable of describing some of the other key ...
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Ornstein–Uhlenbeck process with quadratic killing

Journal of Applied Probability, 1990
An Ornstein-Uhlenbeck process subject to a quadratic killing rate is analyzed. The distribution for the process killing time is derived, generalizing the analogous result for Brownian motion. The derivation involves the use of Hermite polynomials in a spectral expansion.
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Time-changed Ornstein–Uhlenbeck process

Journal of Physics A: Mathematical and Theoretical, 2015
The Ornstein–Uhlenbeck process is one of the most popular systems used for financial data description. However, this process has also been examined in the context of many other phenomena. In this paper we consider the so-called time-changed Ornstein–Uhlenbeck process, in which time is replaced by an inverse subordinator of general infinite divisible ...
Janusz Gajda, Agnieszka Wyłomańska
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Generalized Ornstein–Uhlenbeck Processes

2011
Generalized Ornstein–Uhlenbeck processes constitute a large class of explicit examples of Markov processes in infinite-dimensional spaces with rich mathematical structures. Those processes may have non-trivial invariant measures, which make them become better candidates for infinite-dimensional reference processes than Levy processes.
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