What are some major applications of stochastic calculus?

Answer 1

Applications can be in physics, chemistry, biology, and economics. The application is to complex systems with numerous interacting variables.

Markov Chain Monte Carlo methods is a frequent application.

Answer 2

The best-known stochastic process to which stochastic calculus is applied is the Wiener processes, which is used for

1) modeling Brownian motion 

2) analyzing physical diffusion processes in space of particles subject to random forces.

3) the Wiener process is also applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates.