A Law of Large Numbers with Convergence Rate based on Nonlinear Expectation Theory and Its Application to Communication Detection
This work addresses detection problems in communication systems with non-i.i.d. signals, but it appears incremental as it builds on existing nonlinear expectation theory for specific applications.
The paper tackles the problem of establishing a law of large numbers with convergence rates for special partial sums in probability spaces, using nonlinear expectation theory to handle uncertainty, and applies it to analyze detection errors in communication systems for non-i.i.d. signals, showing convergence rates for upper probabilities of errors.
In this paper, we establish a new law of large numbers with the rate of convergence for special partial sums in a probability space. The proof relies on nonlinear expectation theory, as the uncertainty of random variables in the special partial sums induces the sublinearity of the expectation. As an application, we apply the new theorem to analyze the feedback channel-based detection problem of non-i.i.d. input signals in communication systems. Specifically, we investigate the convergence rates of the upper probabilities of the detection errors within the sublinear expectation space.