We consider an ordinary or stochastic nonlinear equation with generalized coefficients as an equation in differentials in the algebra of new generalized functions in the sense of [8]. Consequently, the solution of such an equation is a new generalized function. We formulate conditions under which the solution of a given equation in the algebra of new generalized functions is associated with an ordinary function or process. Moreover the class of all possible associated functions and processes is described.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-3,
author = {Nadzeya V. Bedziuk and Aleh L. Yablonski},
title = {Equations in differentials in the algebra of generalized stochastic processes},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {31-38},
zbl = {1201.60067},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-3}
}
Nadzeya V. Bedziuk; Aleh L. Yablonski. Equations in differentials in the algebra of generalized stochastic processes. Banach Center Publications, Tome 89 (2010) pp. 31-38. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-3/