Displaying similar documents to “On Weak Convergence of Stochastic Processes With Lusin Path Spaces.”

Weak solutions of stochastic differential inclusions and their compactness

Mariusz Michta (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

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

Similarity:

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.

Weak Hölder convergence of processes with application to the perturbed empirical process

Djamel Hamadouche, Charles Suquet (1999)

Applicationes Mathematicae

Similarity:

We consider stochastic processes as random elements in some spaces of Hölder functions vanishing at infinity. The corresponding scale of spaces C 0 α , 0 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 ( X 1 , . . . , X n ) under a natural assumption about the regularity of the marginal distribution function...