{"product_id":"stochastic-processes-applied-probability-a-second-course-renewal-martingales-and-stochastic-calculus-volume-2-9798199634793","title":"Stochastic Processes \u0026 Applied Probability: A Second Course: Renewal, Martingales, and Stochastic Calculus Volume 2","description":"\u003cp\u003e • Author(s): Mir Hossain\u003cbr\u003e • Publisher: Independently Published\u003cbr\u003e • Publisher Imprint: Independently Published\u003cbr\u003e • BISAC: Differential Equations - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eMaster stochastic processes beyond the basics-with clarity, rigor, and real understanding.\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eStochastic Processes \u0026amp; Applied Probability: Volume 2\u003c\/i\u003e is a carefully structured second course designed for college and university students, engineers, quantitative analysts, and self-learners ready to move beyond introductory probability and Markov chains into the deeper mathematics of stochastic modeling.\u003c\/p\u003e\u003cp\u003eBuilding directly on foundational probability and stochastic-process concepts, this volume develops the theory and applications of \u003cb\u003erenewal processes, martingales, Brownian motion, stochastic calculus, stochastic differential equations, diffusion models, filtering, and simulation\u003c\/b\u003e in a clear and accessible style.\u003c\/p\u003e\u003cp\u003eUnlike many advanced probability texts that assume heavy mathematical maturity and skip intermediate reasoning, this book emphasizes \u003cb\u003estep-by-step learning, intuition, and mastery through worked examples\u003c\/b\u003e while maintaining mathematical rigor.\u003c\/p\u003e\u003cp\u003eInside this volume, you will learn: \u003c\/p\u003e\u003cp\u003e- Renewal theory and long-run stochastic behavior\u003cbr\u003e- Renewal functions and the elementary renewal theorem\u003cbr\u003e- Age, residual life, and the inspection paradox\u003cbr\u003e- Martingales and conditional expectation as working tools\u003cbr\u003e- Filtrations, stopping times, and optional stopping\u003cbr\u003e- Martingale convergence and inequalities\u003cbr\u003e- Brownian motion and sample-path behavior\u003cbr\u003e- The It� integral and stochastic integration\u003cbr\u003e- It�'s formula and stochastic calculus\u003cbr\u003e- Stochastic differential equations (SDEs)\u003cbr\u003e- Diffusions and the Fokker-Planck equation\u003cbr\u003e- Hidden Markov models and filtering methods\u003cbr\u003e- Stochastic simulation and computational probability\u003c\/p\u003e\u003cp\u003eThis book features: \u003c\/p\u003e\u003cp\u003eClear explanations with minimal unnecessary abstraction\u003cbr\u003eFully worked examples throughout\u003cbr\u003eDiagnostic reviews and prerequisite checks\u003cbr\u003eCommon-trap and mistake-prevention sections\u003cbr\u003ePractice, Apply, and Challenge problem sets\u003cbr\u003eStep-by-step solutions\u003cbr\u003eFormula summaries and reference material\u003cbr\u003eSelf-study and classroom-friendly organization\u003c\/p\u003e\u003cp\u003eWhether you are studying \u003cb\u003eprobability, applied mathematics, statistics, quantitative finance, machine learning, operations research, engineering, or stochastic modeling\u003c\/b\u003e, this book provides a rigorous yet approachable pathway into modern stochastic processes and applied probability.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eVolume 2 continues the journey from foundational stochastic models to the powerful tools used in contemporary science, engineering, finance, and data-driven systems.\u003c\/b\u003e\u003c\/p\u003e","brand":"Independently Published","offers":[{"title":"Paperback","offer_id":47968511066263,"sku":"9798199634793","price":2744.0,"currency_code":"INR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9798199634793.webp?v=1782918332","url":"https:\/\/atlanticbooks.com\/products\/stochastic-processes-applied-probability-a-second-course-renewal-martingales-and-stochastic-calculus-volume-2-9798199634793","provider":"Atlantic Books","version":"1.0","type":"link"}