Continuous everywhere nondifferentiable nowhere

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SUMMARY

Everywhere continuous, nowhere differentiable functions, particularly those related to Brownian motion, have significant applications in physics, chemistry, and biology. These functions serve as sample paths for Brownian motions, which are crucial in modeling stochastic processes in engineering. Additionally, they are utilized in the financial sector for modeling derivative securities, where short-term returns are approximately normally distributed. Key literature includes "Brownian Motion and Stochastic Flow Systems" by J. Michael Harrison and "Financial Calculus" by Baxter and Rennie.

PREREQUISITES
  • Understanding of Brownian motion and stochastic processes
  • Familiarity with derivative securities and their pricing models
  • Knowledge of continuous functions in mathematical analysis
  • Basic principles of probability and normal distribution
NEXT STEPS
  • Research the mathematical properties of Brownian motion
  • Explore stochastic calculus applications in engineering
  • Study the pricing models for derivative securities using "Financial Calculus"
  • Investigate the implications of continuous functions in real-world phenomena
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Mathematicians, physicists, engineers, financial analysts, and anyone interested in the applications of continuous functions and stochastic processes in various scientific fields.

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Do everywhere continuous, nowhere differentiable functions realistically model anything in physics, chemistry, or biology ?
Do such functions have applications to those sciences ?
 
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neginf said:
Do everywhere continuous, nowhere differentiable functions realistically model anything in physics, chemistry, or biology ?
Do such functions have applications to those sciences ?

Certain types of functions of this sort are the sample paths of Brownian motions.

These models are also used to model derivative securities since short term returns on securities are approximately normally distributed.

In engineering problems continuous Brownian motions are commonly used to model stochastic processes.

A great book on Brownian motion is "Brownian Motion and Stochastic Flow Systems" by J. Michael Harrison

Also you might like "Financial Calculus" by Baxter and Rennie for derivative securities pricing.
 

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