The paper is concerned with the problem of existence of explosive solutions for a class of nonlinear parabolic Itô equations. Under some sufficient conditions on the initial state and the coefficients, it is proven by the method of auxiliary functionals that there exist explosive solutions with positive probability. The main results are presented in Theorems 3.1 and 3.2 under different sets of conditions. An example is given to illustrate some application of the second theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-5,
author = {Pao-Liu Chow},
title = {Existence of explosive solutions to some nonlinear parabolic It\^o equations},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {73-80},
zbl = {1322.60107},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-5}
}
Pao-Liu Chow. Existence of explosive solutions to some nonlinear parabolic Itô equations. Banach Center Publications, Tome 104 (2015) pp. 73-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-5/