Diffusion Processes, Jump Processes, and Stochastic Differential Equations: An Introduction to the Theory of Stochastic Processes

Stochastic processes are a mathematical model for continuous-time phenomena that exhibit random behavior. They are used in a wide variety of applications, including finance, economics, biology, and physics.

This book provides an to the theory of stochastic processes. It begins with a discussion of the basic concepts of probability theory, and then introduces the different types of stochastic processes. The book then discusses the properties of these processes, and how they can be used to model real-world phenomena.

Diffusion processes are a type of stochastic process that is characterized by the fact that its paths are continuous. This means that the process does not jump from one value to another, but rather changes gradually over time.

Diffusion Processes, Jump Processes, and Stochastic Differential Equations

by Wojbor A. Woyczyński

4.6 out of 5

Language	:	English
File size	:	10126 KB
Screen Reader	:	Supported
Print length	:	418 pages

FREE

Diffusion processes are often used to model phenomena that are driven by a random force. For example, the movement of a particle in a fluid can be modeled by a diffusion process.

Jump processes are a type of stochastic process that is characterized by the fact that its paths are discontinuous. This means that the process can jump from one value to another at any time.

Jump processes are often used to model phenomena that are driven by a sudden event. For example, the arrival of a customer at a store can be modeled by a jump process.

Stochastic differential equations are a type of differential equation that contains a random term. This means that the solution to the equation is a stochastic process.

Stochastic differential equations are often used to model phenomena that are driven by both deterministic and random forces. For example, the movement of a stock price can be modeled by a stochastic differential equation.

Stochastic processes have a wide range of applications in different fields. Some of the most common applications include:

• Finance: Stochastic processes are used to model the movement of stock prices, interest rates, and other financial variables.
• Economics: Stochastic processes are used to model the behavior of economic systems, such as the business cycle and the growth of economies.
• Biology: Stochastic processes are used to model the growth of populations, the spread of diseases, and the evolution of species.
• Physics: Stochastic processes are used to model the behavior of particles in a fluid, the diffusion of heat, and the propagation of waves.

Diffusion processes, jump processes, and stochastic differential equations are powerful tools for modeling a wide variety of real-world phenomena. This book provides an to the theory of stochastic processes, and demonstrates how these processes can be used to model a variety of applications.

Diffusion Processes, Jump Processes, and Stochastic Differential Equations

by Wojbor A. Woyczyński

4.6 out of 5

Language	:	English
File size	:	10126 KB
Screen Reader	:	Supported
Print length	:	418 pages

FREE