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BRADLEY Can a theorem of Csáki and Fischer provide a
E CSÁKI A FÖLDES P RÉVÉSZ Z Shi On the excursions
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applications assume assumption asymptotic Black-Scholes bound Bradley Brownian motion central limit condition conjecture consider constant construction continuous convergence critical defined denote dependent derived dimension distribution dynamics environment equation estimates event Example exists exponent fact field finite fixed formula function give given growth Hence holds implies independent inequality infinite integral intersection interval jumps Lemma limit theorem Markov Math Mathematics measure mixing natural Note obtained option origin particles particular path positive present probability problem proof properties proved random variables random walk refer reinforced Remark respectively satisfies scaling sequence simple solution space standard starting stationary Statistics stochastic stochastic differential equation strictly Suppose surely theory transform turn weight Wiener