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Stochastic Calculus is part of the field of stochastic processes. It covers the following topics:

1] stochastic integrals - definitions, types, properties, relationships;

2] stochastic differential equations - stochastic processes which can be defined in terms of stochastic integrals;

3] general solutions to stochastic differential equations and their properties.

The concept of stochastic integral is very close to the concept of regular, Riemann integral. Just like a Riemann integral of function *f(x)* is the limit of sums

where *max _{n}(t_{n+1} - t_{n})* converges to 0 and each

where

be a stochastic integral of function

In the expression above the

It is just a notation, the expressions above are not differentials. However, the form of the equation has prompted researchers to call it

where

where

- Brownian Motion
- Diffusion
- Geometric Brownian Motion
- Jump-diffusion
- Stochastic Differential Equation
- Stochastic Volatility Modeling

Karatzas, I., & Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus (2nd ed). New York: Springer.

Shreve, S. E. (2004). Stochastic Calculus for Finance II: Continuous-Time Models. New York: Springer.

Oksendal, B. K. (2002). Stochastic Differential Equations: An Introduction with Applications (5th ed). Springer-Verlag Berlin Heidelberg.

Protter, P. E. (2005). Stochastic Integration and Differential Equations (2nd ed). Springer-Verlag Berlin Heidelberg.

Gikhman, I. I., & Skorokhod, A. V. (2007). The Theory of Stochastic Processes III. Springer-Verlag Berlin Heidelberg.

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