Titlebook: Recent Developments in Stochastic Methods and Applications; ICSM-5, Moscow, Russ Albert N. Shiryaev,Konstantin E. Samouylov,Dmitry Confere

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Mean-Square Approximation of Iterated Stochastic Integrals from Strong Exponential Milstein and Wagne integrals are part of the high-order strong numerical methods (with respect to the temporal discretization) for semilinear stochastic partial differential equations with nonlinear multiplicative trace class noise, which are based on the Taylor formula in Banach spaces and exponential formula for t

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A Sequential Test for the Drift of a Brownian Motion with a Possibility to Change a Decisionssibility to change the initial decision at subsequent moments of time for some penalty. Such a testing procedure allows to correct the initial decision if it turns out to be wrong. The test is based on observation of the posterior mean process and makes the initial decision and, possibly, changes i

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Survival Probabilities in Compound Poisson Model with Negative Claims and?Investments as Viscosity Sn) in the corresponding collective risk models involving investments. The equations for the probability of non-ruin as a function of the initial reserve are generated by the infinitesimal operators of corresponding dynamic reserve processes. The direct derivation of such equations is usually accompa

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Stochastic Approach to the Vanishing Viscosity Methodclass parabolic systems such that coefficients of the higher order terms are the same for each equation in the system and to the second class parabolic systems with different higher order term coefficients. With a simple substitution we reduce a system of the first class to a system which may be int

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Cycles in Spaces of Finitely Additive Measures of General Markov Chainsof countably additive measures to the space of finitely additive measures. Cycles of measures generated by the corresponding operator are constructed, and algebraic operations on them are introduced. One of the main results obtained is that any cycle of finitely additive measures can be uniquely dec

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