An algebra M = (M ; ,∨,∧,→, 0, 1) of type 〈2, 2, 2, 2, 0, 0〉 is called a bounded commutative R`-monoid iff (i) (M ; , 1) is a commutative monoid, (ii) (M ;∨,∧, 0, 1) is a bounded lattice, and (iii) x y ≤ z ⇐⇒ x ≤ y → z, (iv) x (x → y) = x ∧ y, for each x, y, z ∈ M . In the sequel, by an R`-monoid we will mean a bounded commutative R`-monoid. (Note that bounded commutative R`-monoids are just bo...

In this paper, we consider multi-dimensional mean reflected backward stochastic differential equations (BSDEs) with possibly non-convex reflection domains along inward normal direction, which were introduced by Briand, Elie and Hu [6] in the scalar case. We first apply a fixed-point argument to establish uniqueness existence result under an additional bounded condition on driver. Then, help of ...

Linear ?-minimax estimators for a bounded normal mean have been explored by Vidakovic and DasGupta (1992). They have found that the risk of linear ?-minimax rules is close to the risk of exact ?-minimax rules. However, the linear rules are not very natural when one estimates bounded parameters. In this paper we explore some modiications of linear rules with two goals in mind: (i) addressing the...