{"title":"Stochastic Processes","description":"\u003cp\u003eStochastic processes examine systems that evolve over time with inherent randomness, making them central to modern probability and statistics. These books cover foundational theory, advanced modeling techniques, and real-world applications, highlighting how random variables change across discrete or continuous stages. This category is essential for those seeking to analyze unpredictable phenomena, from finance and engineering to biology and computer science.\u003c\/p\u003e\u003cp\u003eTo navigate within stochastic processes, consider focusing on domains such as Markov chains, Poisson processes, or Brownian motion. Each subfield emphasizes distinct mathematical tools and problem types. For a broader look at related concepts and methods, the wider Probability \u0026amp; Statistics category connects stochastic processes to other quantitative approaches and theoretical frameworks.\u003c\/p\u003e","products":[{"product_id":"advances-statistic-inference-process-driven-fraction-process-9789819810789-new","title":"Advances Statistic Inference Process Driven Fraction Process","description":"\u003cp\u003eOne of the important problems in studying stochastic phenomena is to develop stochastic models and understand their implications behind the phenomenon. Long range dependence is an important stochastic phenomena and it needs study of special type of stochastic processes for modelling. My earlier book on Statistical Inference for Fractional Diffusion Processes (2010) dealt with several aspects for modelling by fractional Brownian motion. This book will contain my work on parametric and nonparametric inference for processes driven by fractional processes such as fractional Brownian motion, mixed fractional Brownian motion, sub-fractional Brownian motion, alpha-stable noise, fractional Levy process and Gaussian processes.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543606231330,"sku":"9789819810789-new","price":175.81,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789819810789.jpg?v=1776386183"},{"product_id":"intro-probability-2nd-ed-9789819808861-new","title":"Intro to Probability (2nd Ed)","description":"\u003cp\u003eThis edition covers the standard materials to be expected in a course from a calculus-based course in probability. 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Readers of Fractional S(P)DEs will find a unique and comprehensive overview encompassing the theory and the numerics of both ordinary and partial differential equations (SDEs and SPDEs, respectively), driven by fractional Brownian motion.\u003c\/p\u003e\u003cp\u003eWithin this book, both differential equations are considered with fractional noise, while also considering fractional derivatives in the case of SPDEs. Three primary aspects are pursued: \u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eTheory and numerics for rough SPDEs; Optimal control of both SDEs and SPDEs driven by fractional Brownian motions (and their applications); And numerics for time-fractional SPDEs driven by both Gaussian and non-Gaussian noises.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis series of complementary articles, compiled by two internationally renowned scientists, is united by a common application-oriented view of fractional Brownian motion and its stochastic calculus. As such, this book will be particularly useful for mathematicians working in the fields of stochastics applied in Finance and Natural Sciences, as well as those preparing courses on advanced stochastic processes.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543609868578,"sku":"9789819802098-new","price":113.44,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789819802098.jpg?v=1776386316"},{"product_id":"non-uniform-riemann-approach-stochastic-integration-9789819801220-new","title":"The Non-Uniform Riemann Approach to Stochastic Integration","description":"\u003cp\u003eThis is the first book that presents the theory of stochastic integral using the generalized Riemann approach. Readers who are familiar with undergraduate calculus and want to have an easy access to the theory of stochastic integral will find most of this book pleasantly readable, especially the first four chapters. The references to the theory of classical stochastic integral and stochastic processes are also included for the convenience of readers who are familiar with the measure theoretic approach.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543610425634,"sku":"9789819801220-new","price":82.27,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789819801220.jpg?v=1776386348"},{"product_id":"introduction-stochastic-processes-9789814740302-new","title":"Introduction to Stochastic Processes","description":"\u003cp\u003eThe objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts - Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eIn the part on Markov chains, the focus is on the ergodicity. By using the minimal nonnegative solution method, we deal with the recurrence and various types of ergodicity. This is done step by step, from finite state spaces to denumerable state spaces, and from discrete time to continuous time. The methods of proofs adopt modern techniques, such as coupling and duality methods. Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eIn the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. 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This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543628316962,"sku":"9789814689915-new","price":51.1,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814689915.jpg?v=1776387244"},{"product_id":"festschrift-masatoshi-fukushima-9789814596527-new","title":"Festschrift Masatoshi Fukushima","description":"\u003cp\u003eThis book contains original research papers by leading experts in the fields of probability theory, stochastic analysis, potential theory and mathematical physics. There is also a historical account on Masatoshi Fukushima's contribution to mathematics, as well as authoritative surveys on the state of the art in the field.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543660495138,"sku":"9789814596527-new","price":235.05,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814596527.jpg?v=1776388446"},{"product_id":"multifractional-stochastic-fields-9789814525657-new","title":"Multifractional Stochastic Fields","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003eFractional Brownian Motion (FBM) is a very classical continuous self-similar Gaussian field with stationary increments. In 1940, some works of Kolmogorov on turbulence led him to introduce this quite natural extension of Brownian Motion, which, in contrast with the latter, has correlated increments. However, the denomination FBM is due to a very famous article by Mandelbrot and Van Ness, published in 1968. Not only in it, but also in several of his following works, Mandelbrot emphasized the importance of FBM as a model in several applied areas, and thus he made it to be known by a wide community. Therefore, FBM has been studied by many authors, and used in a lot of applications.\u003c\/p\u003e\u003cp\u003eIn spite of the fact that FBM is a very useful model, it does not always fit to real data. This is the reason why, for at least two decades, there has been an increasing interest in the construction of new classes of random models extending it, which offer more flexibility. A paradigmatic example of them is the class of Multifractional Fields. Multifractional means that fractal properties of models, typically, roughness of paths and self-similarity of probability distributions, are locally allowed to change from place to place.\u003c\/p\u003e\u003cp\u003eIn order to sharply determine path behavior of Multifractional Fields, a wavelet strategy, which can be considered to be new in the probabilistic framework, has been developed since the end of the 90's. It is somehow inspired by some rather non-standard methods, related to the fine study of Brownian Motion roughness, through its representation in the Faber-Schauder system. The main goal of the book is to present the motivations behind this wavelet strategy, and to explain how it can be applied to some classical examples of Multifractional Fields. 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Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.Since the first and second editions were published in 1990 and 2005, a number of new results have appeared in the literature. The first two editions contained many unsolved problems and conjectures which have since been settled; this third, revised and enlarged edition includes those new results. In this edition, a completely new part is included concerning Simple Random Walks on Graphs. Properties of random walks on several concrete graphs have been studied in the last decade. 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Paper contributors include colleagues, collaborators and former students of Robert Elliott, many of whom are world-leading experts and have made fundamental and significant contributions to these areas.This book provides new important insights and results by eminent researchers in the considered areas, which will be of interest to researchers and practitioners. The topics considered will be diverse in applications, and will provide contemporary approaches to the problems considered. The areas considered are rapidly evolving. This volume will contribute to their development, and present the current state-of-the-art stochastic processes, analysis, filtering and control.Contributing authors include: H Albrecher, T Bielecki, F Dufour, M Jeanblanc, I Karatzas, H-H Kuo, A Melnikov, E Platen, G Yin, Q Zhang, C Chiarella, W Fleming, D Madan, R Mamon, J Yan, V Krishnamurthy.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543694606626,"sku":"9789814383301-new","price":227.77,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814383301.jpg?v=1776389822"},{"product_id":"nonparametric-statis-method-related-9789814366564-new","title":"Nonparametric Statis Method \u0026 Related...","description":"This volume consists of 22 research papers by leading researchers in Probability and Statistics. Many of the papers are focused on themes that Professor Bhattacharya has published on research. 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It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated Riesz-Fischer theorem for separable Hilbert spaces and the space of Wiener-Ito functionals is drawn out, thus providing a clear insight into the subject.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543699783970,"sku":"9789814366366-new","price":119.69,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814366366.jpg?v=1776390023"},{"product_id":"nonconventional-limit-theorems-random-dynamics-9789813235007-new","title":"Nonconventional Limit Theorems and Random Dynamics","description":"\u003cp\u003eThe book is devoted to limit theorems for nonconventional sums and arrays. 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For such a purpose, we strove to bridge among these interdisciplinary fields in our \u003cem\u003eWorkshop on IDAQP and their Applications\u003c\/em\u003e that was held at the Institute for Mathematical Sciences, National University of Singapore from 3-7 March 2014. 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This book is intended not only for students of mathematics but also for students of natural sciences, engineering, computer science and for science researchers, who possess the basic knowledge of calculus for the mathematical concepts of the textbook and elementary programming skills for the Matlab simulations.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544493097250,"sku":"9789811205736-new","price":113.45,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811205736.jpg?v=1776405311"},{"product_id":"stochastic-pdes-modelling-multiscale-complex-system-9789811200342-new","title":"Stochastic Pdes and Modelling of Multiscale Complex System","description":"\u003cp\u003eThis volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. 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