Numerical solutions of stochastic control problems: Markov chain approximation methodsZhuo Jin a dKy Tran b eGeorge Yin c f
Now that you have seen the example, this should give you an idea of the different concepts related to a Markov chain. But, how and where can you use these theory in real life? With the example that you have seen, you can now answer questions like: "Starting from the state: sleep, ...
Through this example, we demonstrate why more model freedoms are needed, and how Markov chains are extended by Hidden Markov Models (HMM). Following the introduction, we present three basic problems for HMMs and describe their respective solutions. We also introduce the Expectation-Maximization (EM...
In this example, where there are 117,688 feasible solutions, the MCMC chain did not mix until its length was about 10% of the size of the entire space. Recall that, here, the state space is continuous—every move results in another feasible solution, so the traversal of an MCMC chain ...
Results: We propose a method to estimate probabilities of each vertex to belong to the active module based on Markov chain Monte Carlo (MCMC) subnetwork sampling. As an example of the performance of our method on real data, we run it on two gene expression datasets. For the first many-...
problems in, for example, physics, biology, and economics, where the outcome of one experiment can affect the outcome of subsequent experiments. The terminology is not consistent in the literature, and many authors use the same name (Markov chain) for both discrete and continuous cases. We ...
A Markov process or Markov chain is a stochastic process of states that is memoryless, or where the probability of any future state (S_t+1) occurring is only dependent on its current state (S_t), and is independent of any past or future states. ...
In this paper, we have presented a new GMRES method accelerated by vector extrapolation techniques to get the numerical solutions of the stationary probability vector of an irreducible Markov chain, using vector extrapolation techniques. Experimental results on several typical Markov chain problems demonstr...
A Markov decision process (MDP) is a mathematical framework for decision-making in situations where outcomes are partly random and partly controlled by a decision-maker. MDPs help model decisions over time, considering various possible actions and states
We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state of the underlying chain, the integrand must be of a...