A CLT for the third integrated moment of Brownian local time increments
نویسنده
چکیده
Let {Lt ; (x, t) ∈ R1 ×R1 +} denote the local time of Brownian motion. Our main result is to show that for each fixed t ∫ (L t − Lt )3 dx− 12h ∫ (L t − Lt )Lt dx h2 L =⇒ √ 192 (∫ (Lt ) 3 dx )1/2 η as h → 0, where η is a normal random variable with mean zero and variance one that is independent of Lt . This generalizes our previous result for the second moment. We also explain why our approach will not work for higher moments.
منابع مشابه
Central Limit Theorem for the Third Moment in Space of the Brownian Local Time Increments
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