- #1
J.P.
- 5
- 0
Hello,
Given a Brownian Motion process B(t) for 0≤t≤T,
we can write it more explicitly as B(t,ω) where ω[itex]\in[/itex]Ω,
where Ω is the underlying sample space.
My question is: what is the cardinality of Ω. I.e. what is |Ω|?
My thoughts are that it is an uncountable set, based on the observation
that B(t) ~ N(0,t), and thus takes values in the real numbers.
Am I correct, is this simple observation enough, or is a more rigorous
proof needed?
Given a Brownian Motion process B(t) for 0≤t≤T,
we can write it more explicitly as B(t,ω) where ω[itex]\in[/itex]Ω,
where Ω is the underlying sample space.
My question is: what is the cardinality of Ω. I.e. what is |Ω|?
My thoughts are that it is an uncountable set, based on the observation
that B(t) ~ N(0,t), and thus takes values in the real numbers.
Am I correct, is this simple observation enough, or is a more rigorous
proof needed?