Realization of a stochastic process is often called a sample path.


Following is a wiki-definition:

Let (Ω, Σ, P) be a probability space. Let X : I × Ω → S be a stochastic process, where the index set I and state space S are both topological spaces. Then the process X is called sample-continuous (or almost surely continuous, or simply continuous) if the map X(ω) : I → S is continuous as a function of topological spaces for P-almost all ω in Ω.

In many examples, the index set I is an interval of time, [0, T] or [0, +∞), and the state space S is the real line or n-dimensionalEuclidean space Rn.

Though it seems fairly complicated concept, in Gaussian processes, its sample path can easily be found or implemented using several Matlab lines. In this post, I'll focus on implementing GP realization in 2-dimensional space. Extending to higher dimension can easily be done. Following is the resulting figure of GP realization. 

Furthermore, implementing measuring sensory values from the GP-realized field using intperp2 function in Matlab will be introduced. This realization can be used as a reference sensory field in sensor network problems, data fusion problems, and so forth. 

1. main

2. init_stage

3. gp_realization

4. kernel_se

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