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Strictly stationary solutions of ARMA equations in Banach spaces
Strictly stationary solutions ARMA equations Banach spaces Probability
2012/6/21
We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of ARMA equations in Banach spaces with independent and identically distributed noise under certain ass...
Tools for Malliavin calculus in UMD Banach spaces
Malliavin calculus Skorohod integral anticipating processes Meyer inequalities UMD Banach space type 2 space chain rule
2012/4/16
In this paper we study the Malliavin derivatives and Skorohod integrals for processes taking values in an infinite dimensional space. Such results are motivated by their applications to SPDEs and in p...
The vanishing of L2 harmonic one-forms on based path spaces
L2 cohomology Hodge decomposition L2 harmonic forms path space Banach manifold Wiener measure
2012/4/17
We prove the triviality of the first L2 cohomology class of based path spaces of Riemannian manifolds furnished with Brownian motion measure, and the consequent vanishing of L2 harmonic one-forms. We ...
Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces
Branching processes difference-differential equations hyperbolic Brownian motion hyperbolic trigonometry
2011/9/20
Abstract: A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincar\'e half-plane and Poincar\'e disk) is examined. Each particle can split in...
Path properties and regularity of affine processes on general state spaces
affine processes path properties regularity Markov semimartingales
2011/8/30
Abstract: We provide a new proof for regularity of affine processes on general state spaces by methods from the theory of Markovian semimartingales. On the way to this result we also show that the def...
Martingale problems on Banach spaces -- Existence, uniqueness and the Markov property
Martingale solution strong Markov property stochastic partial differential equation
2010/12/6
We study (local) martingale problems on a general separable Banach space E and apply our results to stochastic evolution equations. In particular,we prove that if such an equation is well-posed, then ...