International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 529-542

Symmetrized solutions for nonlinear stochastic differential equations

G. Adomian1 and L. H. Sibul2

1Center for Applied Mathematics, University of Georgia, Athens 30602, Georgia, USA
2Applied Research Laboratory, Pennsylvania State University, University Park 16802, Pennsylvania, USA

Received 15 February 1980; Revised 30 August 1980

Copyright © 1981 G. Adomian and L. H. Sibul. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Solutions of nonlinear stochastic differential equations in series form can be put into convenient symmetrized forms which are easily calculable. This paper investigates such forms for polynomial nonlinearities, i.e., equations of the form Ly+ym=x where x is a stochastic process and L is a linear stochastic operator.