Equations in differentials in the algebra of generalized stochastic processes
Volume 88 / 2010
Banach Center Publications 88 (2010), 31-38
MSC: Primary 34A37, 60H20; Secondary 46F30, 60G20.
DOI: 10.4064/bc88-0-3
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.
