Two-sided reflected Markov-modulated Brownian motion with applications to fluid queues and dividend payouts

In this paper we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time Markov chain. The goal is to compute the stationary distribution of this Markov process, which in addition to the complication of having a stochastic boundary can also include jumps at state change epochs of the underlying Markov chain because of the boundary changes. We give the general theory and then specialize to the case where the underlying Markov chain has two states. Moreover, motivated by an application of optimal dividend strategies, we consider the case where the lower barrier is zero and the upper barrier is subject to control. In this case we generalized earlier results from the case of a reflected Brownian motion to the Markov modulated case.Comment: 22 pages, 1 figur

Useful martingales for stochastic storage processes with L\'{e}vy-type input

In this paper we generalize the martingale of Kella and Whitt to the setting of L\'{e}vy-type processes and show that the (local) martingales obtained are in fact square integrable martingales which upon dividing by the time index converge to zero a.s. and in $L^2$. The reflected L\'{e}vy-type process is considered as an example.Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1112.475

A new formula for some linear stochastic equations with applications

We give a representation of the solution for a stochastic linear equation of the form $X_t=Y_t+\int_{(0,t]}X_{s-} \mathrm {d}{Z}_s$ where $Z$ is a c\'adl\'ag semimartingale and $Y$ is a c\'adl\'ag adapted process with bounded variation on finite intervals. As an application we study the case where $Y$ and $-Z$ are nondecreasing, jointly have stationary increments and the jumps of $-Z$ are bounded by 1. Special cases of this process are shot-noise processes, growth collapse (additive increase, multiplicative decrease) processes and clearing processes. When $Y$ and $Z$ are, in addition, independent L\'evy processes, the resulting $X$ is called a generalized Ornstein-Uhlenbeck process.Comment: Published in at http://dx.doi.org/10.1214/09-AAP637 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

KERJA SAMA INTERNASIONAL DALAM PENCEGAHAN DAN PEMBERANTASAN TINDAK PIDANA PENDANAAN TERORISME MENURUT UNDANG-UNDANG NOMOR 9 TAHUN 2013 TENTANG PENCEGAHAN DAN PEMBERANTASAN TINDAK PIDANA PENDANAAN TERORISME

Tujuan dilakukannya penelitian ini yaitu untuk mengetahui bagaimanakah kerjasama internasional dalam pencegahan dan pemberantasan tindak pidana pendanaan terorisme dan bagaimanakah kerjasama internasional dalam permintaan bantuan pemblokiran berdasarkan daftar terduga teroris dan organisasi teroris dari negara asing atau yurisdiksi asing di mana dengan metode penelitian hukum normatif disimpulkan: 1. Kerjasama internasional dalam pencegahan dan pemberantasan tindak pidana pendanaan terorisme dilaksanakan oleh instansi penegak hukum, PPATK, dan lembaga lain yang terkait dengan pencegahan dan pemberantasan tindak pidana pendanaan terorisme dapat melakukan kerja sama baik dalam lingkup nasional maupun internasional. Dalam rangka mencegah dan memberantas tindak pidana pendanaan terorisme Pemerintah dapat melakukan kerja sama internasional yang meliputi ekstradisi, bantuan hukum timbal balik dalam masalah pidana, dan/atau kerjasama lainnya sesuai dengan ketentuan atas dasar perjanjian atau hubungan baik berdasarkan asas resiprositas. 2. Kerjasama internasional dalam permintaan bantuan pemblokiran berdasarkan daftar terduga teroris dan organisasi teroris dari negara asing atau yurisdiksi asing, maka Negara asing atau yurisdiksi asing dapat menyampaikan permintaan bantuan kepada pemerintah Indonesia untuk melakukan Pemblokiran atas Dana yang diduga berada atau berada di Indonesia milik orang atau Korporasi yang identitasnya tercantum dalam daftar terduga teroris dan organisasi teroris yang dikeluarkan oleh negara asing atau yurisdiksi asing. Sesuai dengan asas resiprositas, Indonesia juga dapat menyampaikan permintaan bantuan kepada negara asing atau yurisdiksi asing untuk melakukan Pemblokiran atas Dana yang patut diduga untuk Tindak Pidana Terorisme yang berada di negara asing atau yurisdiksi asing tersebut.Kata kunci: terorisme; pendanaan terorisme

Unmasking Hercules: Tracing Comedy in Propertius’ Fourth Book

This paper centers on the ninth elegy of Propertius’ fourth book, remaking a neglected case for a reading as paraclausithyron and establishing a further case for siting it in a comic dramatic frame. The aim is to reveal the importance of the comic background to elegy 4.9, particularly in the paraclausithyron topos and the use of a cross-dressed Hercules. The analysis emphasizes the elegy’s sources in stage comedy and contradicts the more typical claim that 4.9 absorbs Hercules into a specifically elegiac framework. Propertius 4.9, altogether, with its myth of Hercules, serves to acclimate an epic figure into the elegiac world, to explore the fluidity of gender in elegy as well as to access the specifics of comedy and mime as a genre important to Propertian poetics. The survey on paraclausithyron and gender play of transvestism in ancient poetry, shall indicate the relation of theatre with Propertius, who draws elegiac settings within the frame of a theatrical scene, veiling Hercules in the appearance of a comic lover

Queue-length balance equations in multiclass multiserver queues and their generalizations

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a departure epoch. The constraint for this result to be valid is that arrivals, and also service completions, with probability one occur individually, i.e., not in batches. We show that it is easy to write down somewhat similar balance equations for {\em multidimensional} queue-length processes for a quite general network of multiclass multiserver queues. We formally derive those balance equations under a general framework. They are called distributional relationships, and are obtained for any external arrival process and state dependent routing as long as certain stationarity conditions are satisfied and external arrivals and service completions do not simultaneously occur. We demonstrate the use of these balance equations, in combination with PASTA, by (i) providing very simple derivations of some known results for polling systems, and (ii) obtaining new results for some queueing systems with priorities. We also extend the distributional relationships for a non-stationary framework

First passage process of a Markov additive process, with applications to reflection problems

In this paper we consider the first passage process of a spectrally negative Markov additive process (MAP). The law of this process is uniquely characterized by a certain matrix function, which plays a crucial role in fluctuation theory. We show how to identify this matrix using the theory of Jordan chains associated with analytic matrix functions. Importantly, our result also provides us with a technique, which can be used to derive various further identities. We then proceed to show how to compute the stationary distribution associated with a one-sided reflected (at zero) MAP for both the spectrally positive and spectrally negative cases as well as for the two sided reflected Markov-modulated Brownian motion; these results can be interpreted in terms of queues with MAP input.Comment: 16 page