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Markov decision process. In mathematics, a Markov decision process ( MDP) is a discrete-time stochastic control process. It provides a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker. MDPs are useful for studying optimization problems solved via ...
These two processes are Markov processes in continuous time, while random walks on the integers and the gambler's ruin problem are examples of Markov processes in discrete time. [42] [43] A famous Markov chain is the so-called "drunkard's walk", a random walk on the number line where, at each step, the position may change by +1 or −1 with ...
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 ...
A stationary Gauss–Markov process is unique [citation needed] up to rescaling; such a process is also known as an Ornstein–Uhlenbeck process. Gauss–Markov processes obey Langevin equations. Basic properties. Every Gauss–Markov process X(t) possesses the three following properties: If h(t) is a non-zero scalar function of t, then Z(t ...
Markov model. In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. [1] It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property ). Generally, this assumption enables reasoning and computation with ...
Piecewise-deterministic Markov process. In probability theory, a piecewise-deterministic Markov process (PDMP) is a process whose behaviour is governed by random jumps at points in time, but whose evolution is deterministically governed by an ordinary differential equation between those times. The class of models is "wide enough to include as ...
Infinitesimal generator (stochastic processes) In mathematics — specifically, in stochastic analysis — the infinitesimal generator of a Feller process (i.e. a continuous-time Markov process satisfying certain regularity conditions) is a Fourier multiplier operator [1] that encodes a great deal of information about the process.
A partially observable Markov decision process ( POMDP) is a generalization of a Markov decision process (MDP). A POMDP models an agent decision process in which it is assumed that the system dynamics are determined by an MDP, but the agent cannot directly observe the underlying state. Instead, it must maintain a sensor model (the probability ...