Functional limit theorems for stochastic integrals with applications to risk processes and to self-financing strategies in a multidimensional market. I

Authors:
Yu. S. Mishura, G. M. Shevchenko and Yu. V. Yukhnovs’kiĭ

Translated by:
N. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **81** (2010).

Journal:
Theor. Probability and Math. Statist. **81** (2010), 131-146

MSC (2010):
Primary 60G44, 60F05, 60B12

DOI:
https://doi.org/10.1090/S0094-9000-2011-00815-0

Published electronically:
January 20, 2011

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study sufficient conditions for the weak convergence of stochastic integrals with respect to processes of bounded variation, martingales, or semimartingales. A semimartingale theorem is extended to the multidimensional case. We apply a limit procedure and pass from processes of bounded variation to risk processes. An "inverse" problem for the weak convergence is also considered.

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Additional Information

**Yu. S. Mishura**

Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine

**G. M. Shevchenko**

Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine

Email:
zhora@univ.kiev.ua

**Yu. V. Yukhnovs’kiĭ**

Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine

Email:
Yuhnovskiy@hq.eximb.com

DOI:
https://doi.org/10.1090/S0094-9000-2011-00815-0

Keywords:
Stochastic integrals,
functional limit theorems,
weak convergence,
semimartingales

Received by editor(s):
July 10, 2009

Published electronically:
January 20, 2011

Additional Notes:
The first two authors are grateful to the European Commissions for support in the framework of the program “Marie Curie Actions”, grant PIRSES-GA-2008-230804

Article copyright:
© Copyright 2011
American Mathematical Society