A Markov process is a stochastic process that satisfies the Markov property, meaning the future state is independent of the past given the present state. It is widely used in various fields to model random systems that evolve over time, where the next state depends only on the current state and not on the sequence of events that preceded it.

Markov Process

Markov process

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

The Markov property is a fundamental characteristic of stochastic processes, where the future state of the process depends only on the present state and not on the sequence of events that preceded it. This memoryless property simplifies the analysis and modeling of complex systems in fields like physics, economics, and artificial intelligence.

Markov property

future state

independent of the past

present state

Random systems are mathematical models that incorporate unpredictability and are often used to describe phenomena that cannot be precisely determined. These systems find applications in various fields such as finance, physics, and computer science to model complex behaviors and uncertainties.

random systems

evolve over time

The 'current state' refers to the present condition or situation of a system, process, or entity, providing a snapshot of its status at a specific point in time. Understanding the current state is crucial for analysis, decision-making, and planning future actions or improvements.

current state

A sequence of events refers to the chronological order in which events occur, providing a framework for understanding the progression and causality within a narrative or process. Recognizing and analyzing sequences of events is crucial for comprehending complex systems, storytelling, and historical analysis, as it helps identify patterns, causes, and effects.

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