Editing Stochastic process (section)

====Indistinguishable====
Two stochastic processes <math>X</math> and <math>Y</math> defined on the same probability space <math>(\Omega,\mathcal{F},P)</math> with the same index set <math>T</math> and set space <math>S</math> are said be '''indistinguishable''' if the following
<div class="center"><math>
P(X_t=Y_t   \text{ for all }  t\in T )=1 ,
</math></div>
holds.<ref name="FrizVictoir2010page571"/><ref name="RogersWilliams2000page130"/> If two <math>X</math> and <math>Y</math> are modifications of each other and are [[almost surely continuous]], then <math>X</math> and <math>Y</math> are indistinguishable.<ref name="JeanblancYor2009page11">{{cite book|author1=Monique Jeanblanc|author1-link= Monique Jeanblanc |author2=Marc Yor|author2-link=Marc Yor|author3=Marc Chesney|title=Mathematical Methods for Financial Markets|url=https://books.google.com/books?id=ZhbROxoQ-ZMC|year=2009|publisher=Springer Science & Business Media|isbn=978-1-85233-376-8|page=11}}</ref>