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The Skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions. In this work, an explicit formula for the Skorokhod map $Gamma_{0,a}$ on $[0,a]$ for any $a>0$ is derived. Specifically, it is shown that on the space $mathcal{D}[0,infty)$ of right-continuous functions with left limits taking values in $mathbb{R}$, $Gamma_{0,a}=Lambda_acirc Gamma_0$, where $Lambda_a:mathcal{D}[0,infty)tomathcal{D}[0,infty)$ is defined by [Lambda_a(phi)(t)=phi(t)-sup_{sin[0,t]}biggl[bigl( phi(s)-abigr)^+wedgeinf_{uin[s,t]}phi(u)biggr]] and $Gamma_0:mathcal{D}[0,infty)tomathcal{D}[0,infty)$ is the Skorokhod map on $[0,infty)$, which is given explicitly by [Gamma_0(psi)(t)=psi(t)+sup_{sin[0,t]}[-psi(s)]^+.] In addition, properties of $Lambda_a$ are developed and comparison properties of $Gamma_{0,a}$ are established.
The Skorokhod map on the half-line has proved to be a useful tool for studying processes with non-negativity constraints. In this work we introduce a measure-valued analog of this map that transforms each element $zeta$ of a certain class of c`{a}dl`
In this paper we use a theorem first proved by S.W.Golomb and a famous inequality by J.B. Rosser and L.Schoenfeld in order to prove that there exists an exact formula for $pi(n)$ which holds infinitely often.
We consider the Skorokhod problem in a time-varying interval. We prove existence and uniqueness for the solution. We also express the solution in terms of an explicit formula. Moving boundaries may generate singularities when they touch. We establish
We study the spectrum reconstruction technique. As is known to all, eigenvalues play an important role in many research fields and are foundation to many practical techniques such like PCA(Principal Component Analysis). We believe that related algori
We introduce a new interacting particles model with blocking and pushing interactions. Particles evolve on the positive line jumping on their own volition rightwards or leftwards according to geometric jumps with parameter q. We show that the model i