  The differential geometry of Kenmotsu manifold is a valuable part of contact
geometry with nice applications in other fields such as theoretical physics. In
fact, its statistical counterpart, that is, Kenmotsu statistical manifold also
has same importance as that of Kenmotsu manifold. Theoretical physicists have
also been looking into the equation of Ricci soliton and Yamabe soliton in
relation with Einstein manifolds, quasi-Einstein manifolds and string theory.
In this research article, first we examine the statistical solitons and Yamabe
soliton on Kenmotsu statistical manifolds with some related examples. Then we
investigate some statistical curvature properties of Kenmotsu statistical
manifolds. Also, we study the statistical solitons on submanifolds of Kenmotsu
statistical manifold with concircular vector field. Furthermore, we discuss the
behavior of almost quasi-Yamabe soliton on submanifolds of Kenmotsu statistical
manifolds endowed with concircular vector field and concurrent vector filed.
Finally, we furnish an example of $5$-dimensional Kenmotsu statistical
manifolds admitting a statistical soliton and almost quasi-Yamabe soliton as
well in the support of this study.
