Limit behavior of functionals of solutions of diffusion type equations

Authors:
G. L. Kulinich, S. V. Kushnirenko and Yu. S. Mishura

Translated by:
N. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **92** (2015).

Journal:
Theor. Probability and Math. Statist. **92** (2016), 93-107

MSC (2010):
Primary 60H10; Secondary 60J60

DOI:
https://doi.org/10.1090/tpms/985

Published electronically:
August 10, 2016

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The asymptotic behavior as of the functionals with an appropriate normalizing factor is studied, where , , is a continuous function, is a locally square integrable function, is an unstable solution of the Itô stochastic differential equation , and is a measurable and bounded function. We find the normalizing factor for the weak convergence of stochastic processes , , for certain classes of these equations. The explicit form of the limit processes is established.

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Additional Information

**G. L. Kulinich**

Affiliation:
Department of General Mathematics, Faculty for Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, 01601, Kyiv, Ukraine

Email:
zag$_$mat@univ.kiev.ua

**S. V. Kushnirenko**

Affiliation:
Department of General Mathematics, Faculty for Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, 01601, Kyiv, Ukraine

Email:
bksv@univ.kiev.ua

**Yu. S. Mishura**

Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, 01601, Kyiv, Ukraine

Email:
myus@univ.kiev.ua

DOI:
https://doi.org/10.1090/tpms/985

Keywords:
Diffusion type processes,
limit behavior of functionals,
unstable solutions of stochastic differential equations

Received by editor(s):
February 24, 2015

Published electronically:
August 10, 2016

Article copyright:
© Copyright 2016
American Mathematical Society