Editing Stochastic process (section)

===Notation===
A stochastic process can be denoted, among other ways, by <math>\{X(t)\}_{t\in T} </math>,<ref name="Brémaud2014page120"/> <math>\{X_t\}_{t\in T} </math>,<ref name="Asmussen2003page408"/> <math>\{X_t\}</math><ref name="Lamperti1977page3">,{{cite book|author=John Lamperti|title=Stochastic processes: a survey of the mathematical theory|url=https://books.google.com/books?id=Pd4cvgAACAAJ|year=1977|publisher=Springer-Verlag|isbn=978-3-540-90275-1|page=3}}</ref> <math>\{X(t)\}</math> or simply as <math>X</math>. Some authors mistakenly write <math>X(t)</math> even though it is an [[abuse of notation#Function notation|abuse of function notation]].<ref name="Klebaner2005page55">{{cite book|author=Fima C. Klebaner|title=Introduction to Stochastic Calculus with Applications|url=https://books.google.com/books?id=JYzW0uqQxB0C|year=2005|publisher=Imperial College Press|isbn=978-1-86094-555-7|page=55}}</ref> For example, <math>X(t)</math> or <math>X_t</math> are used to refer to the random variable with the index <math>t</math>, and not the entire stochastic process.<ref name="Lamperti1977page3"/> If the index set is <math>T=[0,\infty)</math>, then one can write, for example, <math>(X_t , t \geq 0)</math> to denote the stochastic process.<ref name="ChaumontYor2012"/>