Markovtulajdonságú

Markovtulajdonságú refers to the Markov property, a fundamental concept in probability theory and stochastic processes. A stochastic process is said to have the Markov property if the future state of the process depends only on the present state and not on the sequence of events that preceded it. In simpler terms, the past is irrelevant given the present. This characteristic simplifies the analysis of many complex systems.

The Markov property is often described using conditional probability. For a process $X_t$, where $t$ represents time, it means that the probability of $X_{t+1}$ given the entire history up to time $t$ is the same as the probability of $X_{t+1}$ given only the state at time $t$. Mathematically, this can be expressed as $P(X_{t+1} | X_t, X_{t-1}, ..., X_0) = P(X_{t+1} | X_t)$.

Processes exhibiting the Markov property are called Markov processes or Markovian processes. Examples include simple random walks, where the next step depends only on the current position, and certain models of particle diffusion. The Markov property is crucial in fields such as physics, economics, computer science, and biology, enabling the development of predictive models and algorithms. While many real-world phenomena are not strictly Markovian, the approximation is often useful when the dependence on past states is negligible.