On the Weak Convergence of Stochastic Processes.
Monroe D. Donsker (1961)
Mathematica Scandinavica
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Displaying similar documents to “On Weak Convergence of Stochastic Processes With Lusin Path Spaces.”
On the Weak Convergence of Stochastic Processes.
A note on weak solutions to stochastic differential equations
Martin Ondreját, Jan Seidler (2018)
Kybernetika
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We revisit the proof of existence of weak solutions of stochastic differential equations with continuous coeficients. In standard proofs, the coefficients are approximated by more regular ones and it is necessary to prove that: i) the laws of solutions of approximating equations form a tight set of measures on the paths space, ii) its cluster points are laws of solutions of the limit equation. We aim at showing that both steps may be done in a particularly simple and elementary manner. ...
A simple characterization of almost uniform convergence by stochastic convergence.
D. Pachky (1990)
Manuscripta mathematica
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Parametric dependence of the solution processes on the coefficients in McShane's stochastic integral equation systems
J. M. Angulo Ibáñez, R. Gutiérrez Jáimez (1988)
Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
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Weak solutions of stochastic differential inclusions and their compactness
Mariusz Michta (2009)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper, we consider weak solutions to stochastic inclusions driven by a semimartingale and a martingale problem formulated for such inclusions. Using this we analyze compactness of the set of solutions. The paper extends some earlier results known for stochastic differential inclusions driven by a diffusion process.
Tightness of Continuous Stochastic Processes
Michał Kisielewicz (2006)
Discussiones Mathematicae Probability and Statistics
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Some sufficient conditins for tightness of continuous stochastic processes is given. It is verified that in the classical tightness sufficient conditions for continuous stochastic processes it is possible to take a continuous nondecreasing stochastic process instead of a deterministic function one.
A Weak Existence Theorem and Weak Permanence Properties for Strong Liftings.
Klaus Bichteler (1973)
Manuscripta mathematica
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On convergence in some subspaces of generalized functions
S. Pilipović (1979)
Matematički Vesnik
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Subspaces of Weak and Orientated Tschebyshev-Spaces.
Bernd Stockenberg (1977)
Manuscripta mathematica
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Necessary and Sufficiant Conditions on Rates of Convergence in the Multidimensional Central Limit Theorem.
R. Michel (1979)
Manuscripta mathematica
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Weak Hölder convergence of processes with application to the perturbed empirical process
Djamel Hamadouche, Charles Suquet (1999)
Applicationes Mathematicae
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We consider stochastic processes as random elements in some spaces of Hölder functions vanishing at infinity. The corresponding scale of spaces is shown to be isomorphic to some scale of Banach sequence spaces. This enables us to obtain some tightness criterion in these spaces. As an application, we prove the weak Hölder convergence of the convolution-smoothed empirical process of an i.i.d. sample under a natural assumption about the regularity of the marginal distribution function...