## Proceedings of the Bakuriani Colloquium in honour of Yu. V. Prohorov, Bakuriani, Georgia, USSR, 24 February-4 March, 1990 |

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### Contents

The Influence of Extremes Summands on the | 11 |

Generalized Marcinkiewiczs Theorem and Asymptotic Expansions | 30 |

Asymptotic Expansions in Large Deviation Zones for the Distribution | 43 |

Copyright | |

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absolutely continuous Appl arbitrary assume asymptotic Banach space Borel bounded Buldygin central limit theorem compact conditions of Theorem consider constant convex Corollary decomposition defined definition denote equality estimate exists finite following conditions formula Hence Hilbert space holds implies increasing process independent random variables inequality large deviations lim sup linear Liptser martingale Math Mathematical non-negative norm notation Note obtain oo a.s. operator optimal parameter point process probability measures probability space problem Prokhorov proof of Theorem properties Proposition prove Radon measure random element random graph random process random vectors rate function rate of convergence relation respect result right-hand side Russian satisfy condition Sazonov semimartingale Shervashidze Shiryaev solution stationary statistics stochastic differential equations stochastic integral strategy subsets sufficient sums of independent Suppose Theorem 2.1 Theory Probab topology uniformly unique USSR ABSTRACT values VSP/Mokslas weakly Wiener process zero