STOCHASTIC PROCESSES & APPLIED PROBABILITY: A Second Course: Renewal, Martingales, and Stochastic Calculus Volume 2 - Softcover

STOCHASTIC PROCESSES & APPLIED PROBABILITY : A Second Course: Renewal, Martingales, and Stochastic Calculus Volume 2

Taschenbuch. Zustand: Neu. Neuware - Master stochastic processes beyond the basics-with clarity, rigor, and real understanding.Stochastic Processes & Applied Probability: Volume 2 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.Building directly on foundational probability and stochastic-process concepts, this volume develops the theory and applications of renewal processes, martingales, Brownian motion, stochastic calculus, stochastic differential equations, diffusion models, filtering, and simulation in a clear and accessible style.Unlike many advanced probability texts that assume heavy mathematical maturity and skip intermediate reasoning, this book emphasizes step-by-step learning, intuition, and mastery through worked examples while maintaining mathematical rigor.Inside this volume, you will learn: - Renewal theory and long-run stochastic behavior- Renewal functions and the elementary renewal theorem- Age, residual life, and the inspection paradox- Martingales and conditional expectation as working tools- Filtrations, stopping times, and optional stopping- Martingale convergence and inequalities- Brownian motion and sample-path behavior- The Itô integral and stochastic integration- Itô's formula and stochastic calculus- Stochastic differential equations (SDEs)- Diffusions and the Fokker-Planck equation- Hidden Markov models and filtering methods- Stochastic simulation and computational probabilityThis book features: Clear explanations with minimal unnecessary abstractionFully worked examples throughoutDiagnostic reviews and prerequisite checksCommon-trap and mistake-prevention sectionsPractice, Apply, and Challenge problem setsStep-by-step solutionsFormula summaries and reference materialSelf-study and classroom-friendly organizationWhether you are studying probability, applied mathematics, statistics, quantitative finance, machine learning, operations research, engineering, or stochastic modeling, this book provides a rigorous yet approachable pathway into modern stochastic processes and applied probability.Volume 2 continues the journey from foundational stochastic models to the powerful tools used in contemporary science, engineering, finance, and data-driven systems. Artikel-Nr. 9798199634793

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