Here you are asked to find a more precise description of the modulus of continuity of Brownian paths. Prove that   The following is part of what is known as Chung’s law of the iterated logarithm. We...

Here you are asked to find a more precise description of the modulus of continuity of Brownian paths. Prove that

The following is part of what is known as Chung’s law of the iterated logarithm. We will see in Section 40.3 that there exists c₁
such that

for t/λ₂
sufficiently large. Prove that