A stochastic process is a collection of random variables representing the evolution of a system over time, where the future state depends on both the present state and inherent randomness. It is widely used in fields like finance, physics, and biology to model phenomena that evolve unpredictably over time.

Stochastic Process

stochastic process

A random variable is a numerical outcome of a random phenomenon, serving as a bridge between probability theory and real-world scenarios by assigning numerical values to each outcome in a sample space. They are categorized into discrete and continuous types, each with specific probability distributions that describe the likelihood of their outcomes.

random variables

evolution of a system

future state

present state

inherent randomness

fields like finance

Physics is the fundamental science that seeks to understand the nature and behavior of matter and energy in the universe, covering phenomena from the smallest subatomic particles to the largest cosmic structures. It provides the foundational principles that underpin other sciences and technologies, offering insights into the laws governing the physical world and enabling advancements in various fields.

physics

Biology is the scientific study of life and living organisms, encompassing their structure, function, growth, evolution, distribution, and taxonomy. It is a vast and interdisciplinary field that connects with other sciences to understand the complex interactions within ecosystems and the molecular mechanisms of life.

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