# stochastics

- Author: Develata
- Repository: Develata/Deve-Skills
- Version: 20260129203735
- Stars: 0
- Forks: 0
- Last Updated: 2026-02-06
- Source: https://github.com/Develata/Deve-Skills
- Web: https://mule.run/skillshub/@@Develata/Deve-Skills~stochastics:20260129203735

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# Stochastics Department

**Path**: `math-researcher-teacher/domains/stochastics/`

## 🔬 Sub-Domains

### 1. Basic Probability (`basic-probability/`)
*   **Focus**: Axioms, conditional probability, CLT, LLN, common distributions.

### 2. Stochastic Processes (`stochastic-processes/`)
*   **Focus**: Markov Chains, Brownian Motion (Wiener Process), Martingales, Ito Calculus.
*   **Tools**: Monte Carlo simulations.

### 3. Advanced Stochastics (`advanced-stochastics/`)
*   **Focus**:
    *   **Large Deviations**: Rare events, rate functions (Cramér/Sanov).
    *   **Random Matrices**: Wigner Semicircle, Marchenko-Pastur law.
    *   **Random Graphs**: Erdős-Rényi, Watts-Strogatz models (connectivity, phase transitions).

## 🧭 Routing Instructions

*   For **standard probability problems**, go to `basic-probability/`.
*   For **dynamic systems with noise** (stock prices, diffusion), go to `stochastic-processes/`.
*   For **research-level topics** (RMT, LDP, Complex Networks), go to `advanced-stochastics/`.