Stochastic Modeling¶
Stochastic modeling is a statistical approach that incorporates random variables to analyze and predict the behavior of complex systems. It used to model processes that involves undercetainty of randomness, such as a financial markets, weather patterns, or biological systems.
TD;DR¶
Stochastic modeling is a mathematical approach used to predict and analyze systems or processes that involve inherent randomness and uncertainty. Unlike deterministic models, which yield the same outcome for a given set of inputs, stochastic models incorporate random variables, resulting in a range of possible outcomes, each with an associated probability.
Key characteristics¶
- Incorporates Randomness: Stochastic models use random variables to reflect the uncertainty and variability present in real-world systems.
- Probability Distributions: The outcomes are described by probability distributions, which quantify the likelihood of different scenarios.
- Multiple Outcomes: Running the model multiple times with varying random inputs produces a spectrum of possible results, not just a single prediction.
- Scenario Simulation: These models enable simulation of various scenarios, helping users understand the range and probability of potential outcomes.
Stochastic vs. Deterministic Models
| Feature | Stochastic Model | Deterministic Model |
|---|---|---|
| Randomness | Yes (built into the model) | No (inputs and outputs are fixed) |
| # of outcomes | Multiple, each with a probability | Single, repeatable outcome |
| Use case | Systems with inherent uncertainty (e.g., finance, weather) | Predictable systems |
| Example | Monte Carlo Simulation, Markov chains | Simplre interest calculation |