This three-chapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Lévy processes via stochastic integration. The second chapter, by Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgård, concerns Lévy processes reflected at two barriers, where reflection is formulated à la Skorokhod. These processes can be used to model systems with a finite capacity, which is crucial in many real life situations, a most important quantity being the overflow or the loss occurring at the upper barrier. If a process is killed when crossing the boundary, a natural question concerns its lifetime. Deep formulas from fluctuation theory are the key to many classical results, which are reviewed in the third chapter by Frank Aurzada and Thomas Simon. The main part, however, discusses recent advances and developments in the setting where the process is given either by the partial sum of a random walk or the integral of a Lévy process.
Lesson study is a popular professional development approach in Japan whereby teachers collaborate to study content, instruction, and how students solve problems and reach for understanding in order to improve elementary mathematics instruction and learning in the classroom. This book is the first comprehensive look at the system and process of lesson study in Japan. It describes in detail the process of how teachers conducted lesson study--how they collaborated in order to develop a lesson, what they talked about during the process, and what they looked at in order to understand deeply how students were learning. Readers see the planning of a mathematics lesson, as well as how much content knowledge the teachers have. They observe students' problem solving strategies and learn how Japanese teachers prepare themselves to identify those strategies and facilitate the students' discussion. Written for mathematics teachers, educational researchers, school administrators interested in teachers' professional development, and professional developers, this landmark volume provides an in-depth understanding of lesson study that can lead to positive changes in teachers' professional development and in teaching and learning in the United States.
The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications. After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications. Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.
This three-chapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Lévy processes via stochastic integration. The second chapter, by Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgård, concerns Lévy processes reflected at two barriers, where reflection is formulated à la Skorokhod. These processes can be used to model systems with a finite capacity, which is crucial in many real life situations, a most important quantity being the overflow or the loss occurring at the upper barrier. If a process is killed when crossing the boundary, a natural question concerns its lifetime. Deep formulas from fluctuation theory are the key to many classical results, which are reviewed in the third chapter by Frank Aurzada and Thomas Simon. The main part, however, discusses recent advances and developments in the setting where the process is given either by the partial sum of a random walk or the integral of a Lévy process.
Can a poem save your life? Words are powerful. Insults and rumors can derail a career; a bit of encouragement can give someone the strength to pursue their dreams. When a high school boy skipping class to sketch shoe designs and a taciturn woman drinking a morning beer meet in a Tokyo park, they say little, but the woman bids farewell with an ancient tanka poem. Will the boy figure out the poem’s meaning—and its corresponding response—before it’s too late?
Mikako Nagamine is recruited as a pilot to fight in the interstellar war against a force of alien invaders, leaving behind her one true love. Mikako’s only connection to Noboru Terao, who continues living the life of an ordinary student, is through cell phone text messages. As Mikako travels light years away, it takes longer and longer for Noboru to receive her messages, until finally one arrives eight years and seven months after she sent it…
Seventeen-year-old Suzume lives with her aunt in a quiet port town in Kyushu. One day, on her way to school, she runs into a young man searching for something and follows him to a ruin in the hills. But inside, all she finds is a single white door among the rubble. As if pulled by an invisible force, she reaches out to open it...and begins an epic journey across Japan connecting the past, present, and future. Follow Suzume’s adventure in this novelization of the acclaimed animated film Suzume, written by director Makoto Shinkai.
Die 17-jährige Suzume führt ein ruhiges Leben auf der Insel Kyushu. Bis zu dem Tag, als sie auf einen jungen Mann trifft, der ihr sagt, er sei "auf der Suche nach einer Tür". Suzume folgt ihm zu einer Ruine in den Bergen und stößt tatsächlich auf eine mysteriöse, freistehende Tür. Von einer unsichtbaren Kraft getrieben greift sie nach der Klinke - und stürzt damit ganz Japan ins Unglück. Überall im Land öffnen sich weitere Türen, aus denen zerstörerische Kräfte strömen. Um das Unheil abzuwenden, hat sie nur eine Chance: Sie muss die Türen wieder schließen! --- Dieses spezielle E-Book-Format kann auf allen aktuelleren Tablets und Geräten mit Zoomfunktion gelesen werden. Dein Leseprogramm sollte die Darstellung von Fixed-Image-E-Books im EPUB3- oder mobi/KF8-Format unterstützen. Weitere Informationen findest du auf der Homepage von Egmont Manga. ---
High school junior Suzume runs into a handsome stranger, Souta, who tells her he is looking for a door and asks where he can find ruins in her town. She points him toward a resort that has long fallen past all hope of repair, then thinks better of it and races after him to warn him of the danger of trespassing there. While fruitlessly searching for Souta, Suzume opens a door seemingly to nowhere and finds a starry landscape stretch out on the other side of the frame. Later, at school, she realizes she's the only one who can see an ominous, worm-like colossus emerge from the mountains and rushes back to the ruins where she finds Souta struggling to shut the monster back in the door. Suzume helps Souta close the door on the mythical worm, which is revealed to be the cause of massive earthquakes, never knowing that her involvement would soon leave Souta trapped in the three-legged wooden chair Suzume's late mother crafted for her and send them both on a cross-country race to seal all the worms away and save Japan from devastation.
Hodaka zieht von seiner abgelegenen Heimatinsel in die Megametropole Tokio. Aus finanzieller Not bewirbt er sich als Redakteur bei einem okkulten Magazin – und wird tatsächlich genommen. Seitdem regnet es unaufhörlich... Und dann trifft Hodaka auf Hina – ein Mädchen, das das Wetter kontrollieren kann. Was er nicht weiß: Sie wird sein Leben vollkommen auf den Kopf stellen!
Taki hat sein erstes Date mit Fräulein Okudera, was jedoch in einem totalen Fiasko endet. Er tröstet sich damit, dass er schon bald wieder die Rollen mit Mitsuha tauschen wird. Doch die beiden sollen danach nie wieder die Plätze miteinander tauschen... Das Rad des Schicksals setzt sich in Bewegung. --- Dieses spezielle E-Book-Format kann auf allen aktuelleren Tablets und Geräten mit Zoomfunktion gelesen werden. Dein Leseprogramm sollte die Darstellung von Fixed-Image-E-Books im EPUB3- oder mobi/KF8-Format unterstützen. Weitere Informationen findest du auf der Homepage von Egmont Manga. ---
Hodaka zieht von seiner abgelegenen Heimatinsel in die Megametropole Tokio. Aus finanzieller Not bewirbt er sich als Redakteur bei einem okkulten Magazin – und wird tatsächlich genommen. Seitdem regnet es unaufhörlich... Und dann trifft Hodaka auf Hina – ein Mädchen, das das Wetter kontrollieren kann. Was er nicht weiß: Sie wird sein Leben vollkommen auf den Kopf stellen! Das emotionale Finale der Serie.
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