Stationary Solutions of the Stochastic Differential Equation dV t =V t -dU t +dL t with Levy Noise
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For a given bivariate Levy process (U t, L t ) t ≥ 0, necessary and sufficient conditions for the existence of a strictly stationary solution of the stochastic differential equation d V t = V t − d U t + d L t are obtained.About:
This article is published in Stochastic Processes and their Applications.The article was published on 2011-01-01 and is currently open access. It has received 36 citations till now. The article focuses on the topics: Stochastic differential equation.read more
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Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
Journal ArticleDOI
On Exponential Functionals of Lévy Processes
Anita Behme,Alexander Lindner +1 more
TL;DR: In this article, the infinitesimal generator of the generalized Ornstein-Uhlenbeck (GOU) process was obtained and it was shown that it is a Feller process.
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Stochastic Volatility of Volatility and Variance Risk Premia
TL;DR: In this paper, the authors introduce a new class of stochastic volatility models which allow for stochastically volatility of volatility (SVV): Volatility modulated non-Gaussian Ornstein-Uhlenbeck (VMOU) processes.
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Stationary infinitely divisible processes
TL;DR: A review of these types, with some new results, is presented in this article, where a review of the types of continuous-time stationary and infinitely divisible processes is presented.
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Distributional properties of solutions of dVt = Vt-dUt + dLt with Lévy noise
TL;DR: For a given bivariate Levy process (Ut, Lt)t = 0, distributional properties of the stationary solutions of the stochastic differential equation dVt = Vt-dUt + dLt are analyzed in this paper, where the expectation and autocorrelation function are obtained in terms of the process (U, L) and in several cases of interest the tail behavior is described.
References
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Limit Theorems for Stochastic Processes
Jean Jacod,Albert N. Shiryaev +1 more
TL;DR: In this article, the General Theory of Stochastic Processes, Semimartingales, and Stochastically Integrals is discussed and the convergence of Processes with Independent Increments is discussed.
Book
Stochastic integration and differential equations
TL;DR: In this article, the authors propose a method for general stochastic integration and local times, which they call Stochastic Differential Equations (SDEs), and expand the expansion of Filtrations.
Book
Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.