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Stochastic Process

4 articles · Page 1 of 1
Model Perspective
Model Perspective
Oct 3, 2025 · Fundamentals

Unlocking the Power of Markov Chains: From Theory to Real-World Applications

Markov Chains are mathematical models where future states depend only on the current state, not past history, and this article explains their core principles—state space, transition matrices, Markov property, steady-state distribution—and showcases practical uses in economics, biology, web ranking, queueing theory, and reinforcement learning.

Markov chainStochastic ProcessTransition Matrix
0 likes · 7 min read
Unlocking the Power of Markov Chains: From Theory to Real-World Applications
Model Perspective
Model Perspective
Oct 22, 2024 · Fundamentals

How Time‑Inhomogeneous Markov Chains Reveal Shifting Social Behaviors

By introducing time‑inhomogeneous Markov chains, this article shows how dynamic transition probabilities can model and predict evolving social behaviors such as online activity levels, illustrating the method with a three‑state user engagement example and visualizing future activity trends over a year.

Markov chainSocial Behavior ModelingStochastic Process
0 likes · 6 min read
How Time‑Inhomogeneous Markov Chains Reveal Shifting Social Behaviors
Model Perspective
Model Perspective
Nov 9, 2022 · Fundamentals

Understanding Markov Chains: From Basics to Convergence and Sampling

This article explains the fundamentals of Markov chains, illustrates their transition matrix with a market example, demonstrates convergence through Python code, and outlines how to use the stationary distribution for sampling in Monte Carlo simulations.

Markov chainMonte CarloStochastic Process
0 likes · 9 min read
Understanding Markov Chains: From Basics to Convergence and Sampling
Model Perspective
Model Perspective
Jun 11, 2022 · Fundamentals

Understanding Markov Chains: From Basics to Real-World Applications

This article introduces Markov chains, explains their definition, transition matrices, examples, Kolmogorov theorem, limiting distributions, and absorbing chains, showing how memoryless stochastic processes model diverse real‑world phenomena.

Absorbing ChainMarkov chainStochastic Process
0 likes · 10 min read
Understanding Markov Chains: From Basics to Real-World Applications