اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAn explicit formula for the Skorokhod map on $[0,a]$
121
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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`
{a}g paths that take values in the space of signed measures on the half-line to a c`{a}dl`{a}g path that takes values in the space of non-negative measures on $[0,infty)$ in such a way that for each $x > 0$, the path $t mapsto zeta_t[0,x]$ is transformed via a Skorokhod map on the half-line, and the regulating functions for different $x > 0$ are coupled. We establish regularity properties of this map and show that the map provides a convenient tool for studying queueing systems in which tasks are prioritized according to a continuous parameter. Three such well known models are the earliest-deadline-first, the shortest-job-first and the shortest-remaining-processing-time scheduling policies. For these applications, we show how the map provides a unified framework within which to form fluid model equations, prove uniqueness of solutions to these equations and establish convergence of scaled state processes to the fluid model. In particular, for these models, we obtain new convergence results in time-inhomogeneous settings, which appear to fall outside the purview of existing approaches.
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
two sets of sufficient conditions on the moving boundaries that guarantee that the variation of the local time of the associated reflected Brownian motion is, respectively, finite and infinite. We also apply these results to study the semimartingale property of a class of two-dimensional reflected Brownian motions.
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
thms should perform better with more accurate spectrum estimation. There was an approximation formula proposed, however, they didnt give any proof. In our research, we show why the formula works. And when both number of features and dimension of space go to infinity, we find the order of error for the approximation formula, which is related to a constant $c$-the ratio of dimension of space and number of features.
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
nvolves a Pieri-type formula for the orthogonal group. We prove that the two extreme cases - q=0 and q=1 - lead respectively to a random tiling model studied by Borodin and Kuan and to a random matrix model.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
