Remarks on deviation inequalities for functions of infinitely divisible random vectors (Q1872292)

Consider an infinitely divisible \(d\)-dimensional random vector with finite exponential moments. Let \(f\) be a real Lipschitz function. Then the author studies exponential bounds for the decay of the probabilities \(P(f (X) - E (f(X)) \geq x).\) The bound depends on the Lévy measure of \(X\). This approach leads to so-called concentration inequalities for some \(r\)-neighborhood of sets \(A\) with \(P(X \in A) \geq \frac{1}{2}\). The proof is based on explicit covariance formulas for the process \(f (X)\).