Laplace functional

The Laplace functional is a mathematical tool used in the context of stochastic processes, particularly in the field of probability theory and statistical mechanics. It is often utilized to analyze the properties of random processes, especially those that are continuous and have an infinite-dimensional nature, such as point processes and random fields. For a random variable or a stochastic process \(X(t)\), the Laplace functional can be defined in a way that resembles the Laplace transform, but it is typically formulated for measures or point processes.