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...Bismut formula for lions derivative of distribution path dependent sdes a b c jianhai bao panpan ren feng yu wang center applied mathematics tianjin university china department city hongkong kowloon hong kong swansea fabian way skewen sa en uk jianhaibao gmail com rppzoe wangfy tju edu cn july abstract to characterize the regularity in initial which varies as probability measure on space we introduce intrinsic and derivatives measures banach spaces prove chain rule valued random variables by using malliavin calculus establish type functional solutions with drifts when noise term is also so that invalid asymptotic both non degenerate degen erate noises are considered main results this paper generalize improve corresponding ones derived recently literature classical memory mckean vlasov without amssubject classication j keywords introduction stochastic systems evolutions aected micro environment history have been where supported part nnsfc dfg through crc taming uncertainty proting from ...