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A process with this property is said to be Markov or Markovian and known as a Markov process. Two famous classes of Markov process are the Markov chain and Brownian motion. Note that there is a subtle, often overlooked and very important point that is often missed in the plain English statement of the definition. Namely that the statespace of ...
The "Markov" in "Markov decision process" refers to the underlying structure of state transitions that still follow the Markov property. The process is called a "decision process" because it involves making decisions that influence these state transitions, extending the concept of a Markov chain into the realm of decision-making under uncertainty.
Daniel Wyler Stroock (born March 20, 1940) is an American mathematician, a probabilist.He is regarded and revered as one of the fundamental contributors to Malliavin calculus with Shigeo Kusuoka and the theory of diffusion processes with S. R. Srinivasa Varadhan with an orientation towards the refinement and further development of Itô’s stochastic calculus.
In probability theory, Kelly's lemma states that for a stationary continuous-time Markov chain, a process defined as the time-reversed process has the same stationary distribution as the forward-time process. [1] The theorem is named after Frank Kelly. [2] [3] [4] [5]
A Markov decision process is a Markov chain in which state transitions depend on the current state and an action vector that is applied to the system. Typically, a Markov decision process is used to compute a policy of actions that will maximize some utility with respect to expected rewards.
The renewal process is a generalization of the Poisson process.In essence, the Poisson process is a continuous-time Markov process on the positive integers (usually starting at zero) which has independent exponentially distributed holding times at each integer before advancing to the next integer, +.
Usually the term "Markov chain" is reserved for a process with a discrete set of times, that is, a discrete-time Markov chain (DTMC), [11] but a few authors use the term "Markov process" to refer to a continuous-time Markov chain (CTMC) without explicit mention.
Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. [1] [2] A stationary Gauss–Markov process is unique [citation needed] up to rescaling; such a process is also known as an Ornstein–Uhlenbeck process.