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Science & Mathematics - Probability: Theory and Examples (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 49)

Description

Book Synopsis: This lively introduction to measure-theoretic probability theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. Concentrating on results that are the most useful for applications, this comprehensive treatment is a rigorous graduate text and reference. Operating under the philosophy that the best way to learn probability is to see it in action, the book contains extended examples that apply the theory to concrete applications. This fifth edition contains a new chapter on multidimensional Brownian motion and its relationship to partial differential equations (PDEs), an advanced topic that is finding new applications. Setting the foundation for this expansion, Chapter 7 now features a proof of Itó's formula. Key exercises that previously were simply proofs left to the reader have been directly inserted into the text as lemmas. The new edition re-instates discussion about the central limit theorem for martingales and stationary sequences.

Details

Looking to deepen your understanding of probability theory? Look no further! Probability: Theory and Examples is the ultimate resource for graduate students and researchers in the field. Packed with valuable information and practical examples, this book covers all the essential topics you need to know, from laws of large numbers to ergodic theorems, and much more.

What sets this book apart is its emphasis on real-world applications. We believe that the best way to learn probability is to see it in action. That's why Probability: Theory and Examples includes numerous extended examples that demonstrate how the theory can be applied to solve concrete problems. By seeing the theory come to life, you'll gain a deeper understanding of its principles and be better equipped to tackle real-world challenges.

This fifth edition comes with exciting new additions. A brand-new chapter on multidimensional Brownian motion and its relationship to partial differential equations has been included, catering to the growing demand for advanced topics in the field. Additionally, we've included a proof of Itô's formula in Chapter 7, setting the foundation for the expansion of the book. We've also made key exercises more accessible by directly incorporating them into the text, ensuring a seamless learning experience.

Don't miss out on this invaluable resource. Unlock the power of probability theory and take your understanding to new heights. Get your hands on Probability: Theory and Examples now!

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