Path space measures

Continuous time stochastic processes are defined in terms of a sequence of random variables X_t with a time index t taking values in the uncountable continuous time axis R + https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315381619/bc59463b-6388-442c-a6c2-636b9b4ea73c/content/inequ18_1a.tif"/> . As a result, proving the existence and the uniqueness of their distribution on the set of trajectories requires some sophisticated probabilistic and analytic tools. In contrast with discrete time stochastic processes, we have no explicit descriptions of these probability measures.