A First Course in Stochastic Calculus by Louis-Pierre Arguin (Author)

Publisher: MATHEMATICS

Availability: In Stock
SKU: 57200
Number of Pages: 289
Publication Date: 2021-11-21

Rs.660.00

Rs.845.00

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Description

A First Course in Stochastic Calculus by Louis-Pierre Arguin offers a rigorous introduction to the subject of stochastic processes, focusing on the foundational concepts and tools used in stochastic calculus. Designed for undergraduate students, the book presents key topics such as Brownian motion, stochastic integrals, Itô's Lemma, and stochastic differential equations in a clear and accessible manner. With a strong emphasis on both theory and application, Arguin provides a balanced approach to mathematical rigor and practical problem-solving. The text is complemented by examples, exercises, and illustrations that help solidify the understanding of stochastic processes. It is an ideal resource for students pursuing studies in finance, physics, engineering, and applied mathematics, offering a solid foundation for more advanced topics in stochastic analysis.

Keypoints:

Introduction to Stochastic Processes
The book begins with a thorough introduction to the concept of stochastic processes, laying the groundwork for understanding randomness and uncertainty in mathematical modeling.
Clear Explanation of Brownian Motion
One of the central concepts covered in the book is Brownian motion, with detailed explanations on how this continuous-time stochastic process behaves and its significance in various applications.
Stochastic Integrals and Itô Calculus
Arguin introduces stochastic integrals and Itô's Lemma, providing the necessary tools for dealing with integrals in the context of random processes and explaining their application in various fields.
Stochastic Differential Equations (SDEs)
The book covers the fundamentals of stochastic differential equations, showing how to model systems affected by random influences, which is crucial for disciplines like finance and biology.
Applications to Finance and Physics
Examples and exercises illustrate the practical applications of stochastic calculus, particularly in fields like financial modeling, where stochastic processes are used to model stock prices, and physics, for modeling diffusion.
Mathematical Rigor with Accessible Explanations
Arguin strikes a balance between mathematical rigor and clarity, ensuring that the book remains both challenging and accessible to undergraduate students.
Examples and Exercises
A wide variety of examples and exercises are provided throughout the book, helping students grasp complex concepts through practice and reinforcing the theory with real-world applications.
Step-by-Step Approach
The book takes a step-by-step approach to building up the ideas of stochastic calculus, starting with basic concepts and advancing to more complex topics, making it suitable for students with different levels of background knowledge.
Focus on Theoretical Understanding
Emphasis is placed on developing a solid theoretical understanding of stochastic processes and their applications, making it an excellent preparation for more advanced studies in the field.
Ideal for Undergraduate Students
The book is specifically designed for undergraduate students, offering a clear introduction to stochastic calculus that prepares them for graduate-level studies or practical applications in various disciplines.

Conclusion:

A First Course in Stochastic Calculus by Louis-Pierre Arguin is an excellent resource for undergraduate students looking to understand the principles and applications of stochastic processes. With its clear explanations, rigorous approach, and practical examples, the book provides a solid foundation for students pursuing careers in fields such as finance, engineering, and applied mathematics. By balancing theoretical understanding with real-world applications, this text ensures that students are well-prepared for more advanced studies in stochastic analysis.

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Writer ✤ Louis-Pierre Arguin (Author)

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