Equations in differentials in the algebra of generalized stochastic processes

Nadzeya V. Bedziuk, and Aleh L. Yablonski. "Equations in differentials in the algebra of generalized stochastic processes." Banach Center Publications 88.1 (2010): 31-38. <http://eudml.org/doc/281839>.

@article{NadzeyaV2010,
abstract = {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.},
author = {Nadzeya V. Bedziuk, Aleh L. Yablonski},
journal = {Banach Center Publications},
keywords = {Algebra of generalized functions and stochastic processes; differential equations with generalized coefficients},
language = {eng},
number = {1},
pages = {31-38},
title = {Equations in differentials in the algebra of generalized stochastic processes},
url = {http://eudml.org/doc/281839},
volume = {88},
year = {2010},
}

TY - JOUR
AU - Nadzeya V. Bedziuk
AU - Aleh L. Yablonski
TI - Equations in differentials in the algebra of generalized stochastic processes
JO - Banach Center Publications
PY - 2010
VL - 88
IS - 1
SP - 31
EP - 38
AB - 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.
LA - eng
KW - Algebra of generalized functions and stochastic processes; differential equations with generalized coefficients
UR - http://eudml.org/doc/281839
ER -