Empirical evidence of asset price discontinuities or “jumps” in financial markets has been well documented in the literature. Recently, Aït-Sahalia and Jacod (2009b) defined a general “jump activity index” to describe the degree of jump activities for asset price semimartingales, and...

An urn contains balls of d = 2 colors. At each time n = 1, a ball is drawn and then replaced together with a random number of balls of the same color. Let An =diag (An,1, . . . ,An,d) be the n-th reinforce matrix. Assuming EAn,j = EAn,1 for all n and j, a few CLT's are available for such urns....

This paper deals with empirical processes of the type Cn(B) = n^(1/2) {µn(B) - P(Xn+1 in B

This paper deals with empirical processes of the type Cn(B) = n^(1/2) {µn(B) - P(Xn+1 in B | X1, . . . ,Xn)} , where (Xn) is a sequence of random variables and µn = (1/n)SUM(i=1,..,n) d(Xi) the empirical measure. Conditions for supB|Cn(B)| to converge stably (in particular, in distribution)...

An urn contains balls of d = 2 colors. At each time n = 1, a ball is drawn and then replaced together with a random number of balls of the same color. Let An =diag (An,1, . . . ,An,d) be the n-th reinforce matrix. Assuming EAn,j = EAn,1 for all n and j, a few CLT s are available for such urns....