Appl Math Optim 38:219–238 (1998)
1998 Springer-Verlag New York Inc.
Almost Periodically Distributed Solutions for
Diffusion Equations in Duals of Nuclear Spaces
Department of Mathematics, University of Bucharest,
70109 Bucharest, Romania
Centro de Investigacion en Matematicas,
Apdo Postal 402, Guanajuato, Gto. 36000 Mexico
Abstract. We discuss the problem of the existence of almost periodic in distri-
bution solutions of nuclear space-valued diffusion equations with almost periodic
coefﬁcients. Under a dissipativity condition we prove that the translation of the
unique mean square bounded solution is almost periodically distributed. Similar
results hold in the afﬁne case under mean square stability of the linear part of the
equation if the nuclear space is a component of a special compatible family.
Key Words. Nuclear space, Diffusion equations, Bounded and almost periodic
AMS Classiﬁcation. Primary 60H10, Secondary 60J60.
Stochastic differential equations (SDEs) in duals of nuclear spaces arise in problems of
environmental pollution, neurophysiology, nonlinear ﬁltering, etc. A general model for
nonlinear nuclear space-valued SDEs of diffusion type has been studied by Kallianpur
et al. .
The relevance of nuclear space-valued SDEs instead of Hilbert space-valued SDEs
is explained by the presence of more tractable criteria for weak convergence (see )
This research was supported by CONACYT Grant 1858E9219.