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Spatial Stochastic Processes
This volume has been created in honor of the seventieth birthday of Ted Harris, which was celebrated on January 11th, 1989. The papers rep resent the wide range of subfields of probability theory in which Ted has made profound and fundamental contributions. This breadth in Ted's research complicates the task of putting together in his honor a book with a unified theme. One common thread noted was the spatial, or geometric, aspect of the phenomena Ted investigated. This volume has been organized around that theme, with papers covering four major subject areas of Ted's research: branching processes, percola tion, interacting particle systems, and stochastic flows. These four topics do not· ex...
Stochastic Analysis and Applications to Finance
A collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. It covers the topics ranging from Markov processes, backward stochastic differential equations, stochastic partial differential equations, and stochastic control, to risk measure and risk theory.
Markov Chains and Stochastic Stability
Markov Chains and Stochastic Stability is part of the Communications and Control Engineering Series (CCES) edited by Professors B.W. Dickinson, E.D. Sontag, M. Thoma, A. Fettweis, J.L. Massey and J.W. Modestino. The area of Markov chain theory and application has matured over the past 20 years into something more accessible and complete. It is of increasing interest and importance. This publication deals with the action of Markov chains on general state spaces. It discusses the theories and the use to be gained, concentrating on the areas of engineering, operations research and control theory. Throughout, the theme of stochastic stability and the search for practical methods of verifying suc...
Recent Development In Stochastic Dynamics And Stochastic Analysis
Stochastic dynamical systems and stochastic analysis are of great interests not only to mathematicians but also to scientists in other areas. Stochastic dynamical systems tools for modeling and simulation are highly demanded in investigating complex phenomena in, for example, environmental and geophysical sciences, materials science, life sciences, physical and chemical sciences, finance and economics.The volume reflects an essentially timely and interesting subject and offers reviews on the recent and new developments in stochastic dynamics and stochastic analysis, and also some possible future research directions. Presenting a dozen chapters of survey papers and research by leading experts in the subject, the volume is written with a wide audience in mind ranging from graduate students, junior researchers to professionals of other specializations who are interested in the subject.
Variational Methods For Strongly Indefinite Problems
This unique book focuses on critical point theory for strongly indefinite functionals in order to deal with nonlinear variational problems in areas such as physics, mechanics and economics. With the original ingredients of Lipschitz partitions of unity of gage spaces (nonmetrizable spaces), Lipschitz normality, and sufficient conditions for the normality, as well as existence-uniqueness of flow of ODE on gage spaces, the book presents for the first time a deformation theory in locally convex topological vector spaces. It also offers satisfying variational settings for homoclinic-type solutions to Hamiltonian systems, Schrödinger equations, Dirac equations and diffusion systems, and describes recent developments in studying these problems. The concepts and methods used open up new topics worthy of in-depth exploration, and link the subject with other branches of mathematics, such as topology and geometry, providing a perspective for further studies in these areas. The analytical framework can be used to handle more infinite-dimensional Hamiltonian systems.
Advances in Interdisciplinary Applied Discrete Mathematics
Focuses on fields such as consensus and voting theory, clustering, location theory, mathematical biology, and optimization that have seen an upsurge of exciting works over the years using discrete models in modern applications. This book discusses advances in the fields, highlighting the approach of cross-fertilization of ideas across disciplines.
Amplitude Equations For Stochastic Partial Differential Equations
Rigorous error estimates for amplitude equations are well known for deterministic PDEs, and there is a large body of literature over the past two decades. However, there seems to be a lack of literature for stochastic equations, although the theory is being successfully used in the applied community, such as for convective instabilities, without reliable error estimates at hand. This book is the first step in closing this gap.The author provides details about the reduction of dynamics to more simpler equations via amplitude or modulation equations, which relies on the natural separation of time-scales present near a change of stability.For students, the book provides a lucid introduction to the subject highlighting the new tools necessary for stochastic equations, while serving as an excellent guide to recent research.
Perspectives in Mathematical Sciences
1. Periodic boundary problems for analytic function including automorphic functions / Haitao Cai and Jian-Ke Lu -- 2. Subharmonic bifurcations and chaos for a model of micro-cantilever in MEMS / Yushu Chen, Liangqiang Zhou and Fangqi Chen -- 3. Canonical sample spaces for random dynamical systems / Jinqiao Duan, Xingye Kan and Bjorn Schmalfuss -- 4. Epidemic propagation dynamics on complex networks / Xinchu Fu ... [et al.] -- 5. Inverse problems for equations of parabolic type / Zhibin Han, Yongzhong Huang and Ming Jian -- 6. The existence and asymptotic properties of nontrivial solutions of nonlinear (2 - q)-Laplacian type problems with linking geometric structure / Gongbao Li and Zhaofen S...
Dependence in Probability and Statistics
This book gives an account of recent developments in the field of probability and statistics for dependent data. It covers a wide range of topics from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. There is a section on statistical estimation problems and specific applications. The book is written as a succession of papers by field specialists, alternating general surveys, mostly at a level accessible to graduate students in probability and statistics, and more general research papers mainly suitable to researchers in the field.
