Tag: Stochastic

Free Download Numerical Approximations of Stochastic Maxwell Equations: via Structure-Preserving Algorithms (Lecture Notes in Mathematics) by Chuchu Chen, Jialin Hong, Lihai Ji
English | January 5, 2024 | ISBN: 981996685X | 304 pages | MOBI | 66 Mb
The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems.

Free Download Anatolij V. Skorochod, "Lectures on the Theory of Stochastic Processes"
English | ISBN: 9067642061 | 2018 | 189 pages | PDF | 15 MB
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Free Download Continuous Parameter Markov Processes and Stochastic Differential Equations (Graduate Texts in Mathematics, 299) by Rabi Bhattacharya, Edward C. Waymire
English | November 17, 2023 | ISBN: 3031332946 | 521 pages | MOBI | 110 Mb
This graduate text presents the elegant and profound theory of continuous parameter Markov processes and many of its applications. The authors focus on developing context and intuition before formalizing the theory of each topic, illustrated with examples.

Free Download Stochastic Flood Forecasting System: The Middle River Vistula Case Study By Renata J. Romanowicz, Marzena Osuch (eds.)
2015 | 198 Pages | ISBN: 3319188534 | PDF | 9 MB
This book presents the novel formulation and development of a Stochastic Flood Forecasting System, using the Middle River Vistula basin in Poland as a case study. The system has a modular structure, including models describing the rainfall-runoff and snow-melt processes for tributary catchments and the transformation of a flood wave within the reach. The sensitivity and uncertainty analysis of the elements of the study system are performed at both the calibration and verification stages. The spatial and temporal variability of catchment land use and river flow regime based on analytical studies and measurements is presented. A lumped parameter approximation to the distributed modelling of river flow is developed for the purpose of flow forecasting. Control System based emulators (Hammerstein-Wiener models) are applied to on-line data assimilation. Medium-range probabilistic weather forecasts (ECMWF) and on-line observations of temperature, precipitation and water levels are used to prolong the forecast lead time. The potential end-users will also benefit from a description of social vulnerability to natural hazards in the study area.

Free Download Dmitry G. Arseniev, "Adaptive Stochastic Methods: In Computational Mathematics and Mechanics"
English | ISBN: 3110553643 | 2018 | 290 pages | EPUB | 24 MB
This monograph develops adaptive stochastic methods in computational mathematics. The authors discuss the basic ideas of the algorithms and ways to analyze their properties and efficiency. Methods of evaluation of multidimensional integrals and solutions of integral equations are illustrated by multiple examples from mechanics, theory of elasticity, heat conduction and fluid dynamics.

Free Download Stochastic versus Deterministic Systems of Iterative Processes
English | 2024 | ISBN: 9811287473 | 355 Pages | PDF (True) | 5 MB
Continuous state dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend on mode of convergence. Second, the basic probabilistic and statistical properties, namely, the behavior of mean, variance, moments of solutions are described as qualitative/quantitative properties of solution process. We observe that the nature of probability distribution or density functions possess the qualitative/quantitative properties of iterative prosses as a special case. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.

Free Download Problems And Solutions In Stochastic Calculus With Applications
English | 2025 | ISBN: 1800615574 | 484 Pages | PDF (True) | 10 MB
Problems and Solutions in Stochastic Calculus with Applications exposes readers to simple ideas and proofs in stochastic calculus and its applications. It is intended as a companion to the successful original title Introduction to Stochastic Calculus with Applications (Third Edition) by Fima Klebaner. The current book is authored by three active researchers in the fields of probability, stochastic processes, and their applications in financial mathematics, mathematical biology, and more. The book features problems rooted in their ongoing research. Mathematical finance and biology feature pre-eminently, but the ideas and techniques can equally apply to fields such as engineering and economics.

Free Download Probability Theory II: Stochastic Calculus
English | 2024 | ISBN: 3031631927 | 329 Pages | PDF EPUB (True) | 34 MB
This book offers a modern approach to the theory of continuous-time stochastic processes and stochastic calculus. The content is treated rigorously, comprehensively, and independently. In the first part, the theory of Markov processes and martingales is introduced, with a focus on Brownian motion and the Poisson process. Subsequently, the theory of stochastic integration for continuous semimartingales was developed. A substantial portion is dedicated to stochastic differential equations, the main results of solvability and uniqueness in weak and strong sense, linear stochastic equations, and their relation to deterministic partial differential equations. Each chapter is accompanied by numerous examples. This text stems from over twenty years of teaching experience in stochastic processes and calculus within master’s degrees in mathematics, quantitative finance, and postgraduate courses in mathematics for applications and mathematical finance at the University of Bologna. The book provides material for at least two semester-long courses in scientific studies (Mathematics, Physics, Engineering, Statistics, Economics, etc.) and aims to provide a solid background for those interested in the development of stochastic calculus theory and its applications. This text completes the journey started with the first volume of Probability Theory I – Random Variables and Distributions, through a selection of advanced classic topics in stochastic analysis.

Free Download Stochastic Space-Time Models and Limit Theorems by L. Arnold, P. Kotelenez
English | PDF | 1985 | 269 Pages | ISBN : 902772038X | 16.9 MB
Approach your problems from It isn’t that they can’t see the right end and begin with the solution. the answers. Then one day, It is that they can’t see the perhaps you will find the problem. final question. G.K. Chesterton. The Scandal ‘The Hermit Clad 1n Crane of Father Brown ‘The Point of Feathers’ in R. van Gulik’s a Pin’. The Chinese Maze Murders. Growing specialisation and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches wich were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD" , "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Free Download Stochastic Optimization Methods by Kurt Marti
English | PDF | 2005 | 317 Pages | ISBN : 3540222723 | 10.3 MB
Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.