Existence of explosive solutions to some nonlinear parabolic Itô equations
Volume 105 / 2015
Banach Center Publications 105 (2015), 73-80
MSC: Primary 60H15; Secondary 60H05.
DOI: 10.4064/bc105-0-5
Abstract
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.
