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Existence of explosive solutions to some nonlinear parabolic Itô equations

Volume 105 / 2015

Pao-Liu Chow 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.

Authors

  • Pao-Liu ChowDepartment of Mathematics
    Wayne State University
    Detroit, Michigan, USA
    e-mail

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