Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma, and applications to local times

Central limit theorem for the third moment in space of the Brownian local time increments

“…Finally, the result follows from the inequalities for the local time proved by Barlow and Yor in [1].…”

Stochastic Navier-Stokes Equations

“…Proof: Let v ε (·) be the solution of the stochastic equation 4) and ν ε be the law of v ε (·) on the C([0, T ]; H). Then by [16], we know that ν ε satisfies a large deviation principle with the rate function I(·).…”

“…To estimate the stochastic integral term, we will use the following remarkable result from [5], [4] that there exists a universal constant c such that, for any p ≥ 2 and for any continuous martingale (M t ) with M 0 = 0, one has…”

Distribution function inequalities for the density of the area integral

“…Then by this fact, and (5.4) with A replaced by £3 A and £ replaced by / _^i \ e' 5 we obtain I < (7iexp ( -3-) \Q\. To control II, we proceed as before.…”