Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.

The present volume is dedicated to Marek Musiela, an eminent scholar and practitioner who is perhaps best-known for his important contributions to problems of derivative pricing, theory of term structure of interest rates, theory of defaultable securities and other topics in modern mathematical finance. It includes 25 research papers by 47 authors, established experts and newcomers alike, that cover the whole range of the "hot" topics in the discipline. The contributed articles not only give a clear picture about what is going on in this rapidly developing field of knowledge but provide methods ready for practical implementation. They also open new prospects for further studies in risk management, portfolio optimization and financial engineering.

This book presents a unified treatment of various problems arising in the theory of financial markets with friction. It gives a succinct account of arbitrage theory for financial markets with and without transaction costs based on a synthesis of ideas.

This volume constitutes refereed proceedings of the 5th International Conference on Digital Transformation and Global Society, DTGS 2020, held in St. Petersburg, Russia, in June 2020. Due to the COVID-19 pandemic the conference was held online. The 30 revised full papers and 6 short papers presented in the volume were carefully reviewed and selected from 108 submissions. The papers are organized in topical sections on e-society: virtual communities and online activism; e-society: computational social science; e-polity: governance and politics on the Internet; e-city: smart cities and urban governance; e-economy: digital economy and consumer behavior; e-humanities: digital culture and education; e-health: international workshop "E-Health: 4P-medicine & Digital Transformation".

This two volume set (CCIS 858 and CCIS 859) constitutes the refereed proceedings of the Third International Conference on Digital Transformation and Global Society, DTGS 2018, held in St. Petersburg, Russia, in May/June 2018. The 75 revised full papers and the one short paper presented in the two volumes were carefully reviewed and selected from 222 submissions. The papers are organized in topical sections on e-polity: smart governance and e-participation, politics and activism in the cyberspace, law and regulation; e-city: smart cities and urban planning; e-economy: IT and new markets; e-society: social informatics, digital divides; e-communication: discussions and perceptions on the social media; e-humanities: arts and culture; International Workshop on Internet Psychology; International Workshop on Computational Linguistics.

This two volume set (CCIS 858 and CCIS 859) constitutes the refereed proceedings of the Third International Conference on Digital Transformation and Global Society, DTGS 2018, held in St. Petersburg, Russia, in May/June 2018. The 75 revised full papers and the one short paper presented in the two volumes were carefully reviewed and selected from 222 submissions. The papers are organized in topical sections on e-polity: smart governance and e-participation, politics and activism in the cyberspace, law and regulation; e-city: smart cities and urban planning; e-economy: IT and new markets; e-society: social informatics, digital divides; e-communication: discussions and perceptions on the social media; e-humanities: arts and culture; International Workshop on Internet Psychology; International Workshop on Computational Linguistics.

This book constitutes the refereed proceedings of the Second International Conference on Digital Transformation and Global Society, DTGS 2017, held in St. Petersburg, Russia, in June 2017. The 34 revised full papers and three revised short papers presented were carefully reviewed and selected from 134 submissions. The papers are organized in topical sections on eSociety: social media analysis; eSociety: ICTs in education and science; eSociety: legal, security and usability issues; ePolity: electronic governance and electronic participation; ePolity: politics of cyberspace; eCity: urban planning and smart cities; eHealth: ICTs in public health management; eEconomy and eFinance: finance and knowledge management.

This book constitutes the refereed proceedings of the First International Conference on Digital Transformation and Global Society, DTGS 2016, held in St. Petersburg, Russia, in June 2016. The 43 revised full papers and 15 revised short papers, presented together with 3 poster papers and an invited paper were carefully reviewed and selected from 157 submissions. The papers are organized in topical sections on eSociety: New Social Media Studies; eSociety: eGovernment and eParticipation: Perspectives on ICTs in Public Administration and Democracy; eKnowledge: ICTs in Learning and Education Management; eCity: ICTs for Better Urban (Rural) Planning and Living; eHealth: ICTs in Healthcare; eScience: Big Data Complex Calculations.

The present volume is dedicated to Marek Musiela, an eminent scholar and practitioner who is perhaps best-known for his important contributions to problems of derivative pricing, theory of term structure of interest rates, theory of defaultable securities and other topics in modern mathematical finance. It includes 25 research papers by 47 authors, established experts and newcomers alike, that cover the whole range of the "hot" topics in the discipline. The contributed articles not only give a clear picture about what is going on in this rapidly developing field of knowledge but provide methods ready for practical implementation. They also open new prospects for further studies in risk management, portfolio optimization and financial engineering.

The book is the first monograph on this highly important subject.

In many complex systems one can distinguish "fast" and "slow" processes with radically di?erent velocities. In mathematical models based on di?er- tialequations, suchtwo-scalesystemscanbedescribedbyintroducingexpl- itly a small parameter?on the left-hand side ofstate equationsfor the "fast" variables, and these equationsare referredto assingularly perturbed. Surpr- ingly, this kind of equation attracted attention relatively recently (the idea of distinguishing "fast" and "slow" movements is, apparently, much older). Robert O'Malley, in comments to his book, attributes the originof the whole historyofsingularperturbationsto the celebratedpaperofPrandtl 79]. This was an extremely short note, the text of his talk at the Third International Mathematical Congress in 1904: the young author believed that it had to be literally identical with his ten-minute long oral presentation. In spite of its length, it had a tremendous impact on the subsequent development. Many famous mathematicians contributed to the discipline, having numerous and important applications. We mention here only the name of A. N. Tikhonov, whodevelopedattheendofthe1940sinhisdoctoralthesisabeautifultheory for non-linear systems where the fast variables can almost reach their eq- librium states while the slow variables still remain near their initial values: the aerodynamics of a winged object like a plane or the "Katiusha" rocket may serve an example of such a system. It is generally accepted that the probabilistic modeling of real-world p- cesses is more adequate than the deterministic modeling.

This volume constitutes refereed proceedings of the 6th International Conference on Digital Transformation and Global Society, DTGS 2021, held as a virtual event in June 2021. Due to the COVID-19 pandemic the conference was held online. The 34 revised full papers and 4 short papers presented in the volume were carefully reviewed and selected from 95 submissions. The papers are organized in topical sections on eSociety: social informatics and digital inclusion issues; ePolity: e-governance and regulation; eCity: smart cities and urban planning; eHumanities: digital education and research methods; eCommunication: online discources and attitudes; eEconomy: challenges of the COVID-19 pandemic; eEconomy: e-commerce research.

This volume constitutes the refereed proceedings of the 4th International Conference on Digital Transformation and Global Society, DTGS 2019, held in St. Petersburg, Russia, in June 2019.The 56 revised full papers and 9 short papers presented in the volume were carefully reviewed and selected from 194 submissions. The papers are organized in topical sections on e-polity: governance; e-polity: politics online; e-city: smart cities and urban planning; e-economy: online consumers and solutions; e-society: computational social science; e-society: humanities and education; international workshop on internet psychology; international workshop on computational linguistics.