Displaying similar documents to “The central limit theorem for stochastic integrals.”

Approximation of stochastic differential equations driven by α-stable Lévy motion

Aleksander Janicki, Zbigniew Michna, Aleksander Weron (1997)

Applicationes Mathematicae

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In this paper we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to α-stable Lévy motion. We prove an appropriate weak limit theorem, which does not follow from known results on stability properties of stochastic differential equations driven by semimartingales. It assures convergence in law in the Skorokhod topology of sequences of approximate solutions and justifies discrete time schemes applied in computer...

Modelling Real World Using Stochastic Processes and Filtration

Peter Jaeger (2016)

Formalized Mathematics

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First we give an implementation in Mizar [2] basic important definitions of stochastic finance, i.e. filtration ([9], pp. 183 and 185), adapted stochastic process ([9], p. 185) and predictable stochastic process ([6], p. 224). Second we give some concrete formalization and verification to real world examples. In article [8] we started to define random variables for a similar presentation to the book [6]. Here we continue this study. Next we define the stochastic process. For further...

Strong solutions for stochastic differential equations with jumps

Zenghu Li, Leonid Mytnik (2011)

Annales de l'I.H.P. Probabilités et statistiques

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General stochastic equations with jumps are studied. We provide criteria for the uniqueness and existence of strong solutions under non-Lipschitz conditions of Yamada–Watanabe type. The results are applied to stochastic equations driven by spectrally positive Lévy processes.

On Talagrand's Admissible Net Approach to Majorizing Measures and Boundedness of Stochastic Processes

Witold Bednorz (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We show that the main result of [1] on sufficiency of existence of a majorizing measure for boundedness of a stochastic process can be naturally split in two theorems, each of independent interest. The first is that the existence of a majorizing measure is sufficient for the existence of a sequence of admissible nets (as recently introduced by Talagrand [5]), and the second that the existence of a sequence of admissible nets is sufficient for sample boundedness of a stochastic 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.