文档介绍：134 3. Financial MarketsThe correlation functions can be approximated by using the standard decoup-ling procedureGx(t)Gx(t)Gy(t?)Gy(t?)Gx(t)Gy(t?)Gx(t)Gy(t?)+Gx(t)Gy(t?)Gx(t)Gy(t?).()Formally, the correlation functionGx(t)Gx(t?) is equivalent to the jointprobabilityp(x, t;x?,t?)=p(x, t|x?,t?)p(x?,t?). In a stationary market,the unconditional probability distribution functionp(x?,t?) is a slowly vary-ing pared with the conditional probabilityp(x, t|x?,t?) thatdepends strongly on the logarithmic price di?erence?=x?x?. Therefore,the probability densityp(x?,t?) is assumed to be a constant that may beincorporated into the coe?cients of the therefore obtain a series expansion of the slow memory in terms of theconditional probability densityp(x, t|x?,t?) starting with the second absence of linear contributions is a consequence of the orthogonalityrelation (). We focus in the following discussion on the second-orderterm of (), which seems to be the leading term of a schematic expansionofKslowxy(t?t?). Higher contributions can be treated in the same way. Due tothe decoupling, we getKslowxy(t?t?)=?xxyyBxxxByyyp(x?,t|y?,t?)p(x??,t|y??,t?)=?xxyyBxxxByyyp(x?,t|y??,t?)p(x??,t|y?,t?).()This memory can be simpli?ed further by considering some reasonableassumptions about the structure ofBxxx. In particular, we expect ()tobe dominated by coe?cientsBxxxreferring to in?nitesimally neighboringlogarithmic pricesx,x?, andx??. If we take into account the expected symme-try ofp(x, t|x?,t?)=p(?x, t|x?,t?), we arrive at the general representationKslowxx(t?t?)=??n=0?n???x??2np(x, t|x?,t?)2.()Note that because of the symmetry mentioned odd powers of?/?xmustvanish identically. The strength parameters?nof the memory are determinedby the underlying hidden dynamics of the irrelevant degrees of freedom. Thus,after some partial integrations, the evolution equation () can be writtenas?p(x, t|x0,t0)?t=02?2?x2p(x, t|x0,t0)()3The probabi