Mathematics and Statistics
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Mathematics plays a critical role in efforts to understand the nature of the physical universe and in the continuing development of technology. Emphasizing excellence in both research and teaching, the Mathematics & Statistics Department at BU offers a wide range of courses in pure and applied mathematics and statistics at the undergraduate and graduate level. The department has particularly strong groups in dynamical systems and applications, geometry/topology, mathematical physics, number theory, and probability and statistics.
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Department chair: Tasso Kaper
Campus address: 111 Cummington Street
Phone: 6173532560
Fax: 6173538100
Website: www.bu.edu/math/
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Option pricing in ARCHtype models: with detailed proofs
(Freiburger Zentrum für Dateanlyse und Modellbildung, AlbertLudwigsUniversität, Freiburg im Breslau, Germany ( Freiburg Center for Data Analysis and Modeling, AlbertLudwigsUniversität, Freiburg im Wroclaw, Germany), 199503)ARCHmodels have become popular for modelling financial time series. The seem, at first, however, to be incompatible with the option pricing approach of Black, Scholes, Merton et al., because they are discretetime models ... 
A survey of functional laws of the iterated logarithm for selfsimilar processes
(198401)A process X(t) is selfsimilar with index H > 0 if the finitedimensional distributions of X(at) are identical to those of aHX(t) for all a > 0. Consider selfsimilar processes X(t) that are Gaussian or that can be represented ... 
Lévy measures of infinitely divisible random vectors and Slepian inequalities
(199410)We study Slepian inequalities for general nonGaussian infinitely divisible random vectors. Conditions for such inequalities are expressed in terms of the corresponding Levy measures of these vectors. These conditions are ... 
Nonlinear regression of stable random variables
(Institute of Mathematical Statistics, 199111)Let (X1,X2) be an αstable random vector, not necessarily symmetric, with 0<α<2. This article investigates the regression E(X2∣X1=x) for all values of α. We give conditions for the existence of the conditional moment ... 
Generalized powers of strongly dependent random variables
(Cornell University Operations Research and Industrial Engineering, 198411)Generalized powers of strongly dependent random variables 
Stable fractal sums of pulses: the cylindrical case
(199509)A class of αstable, 0\textlessα\textless2, processes is obtained as a sum of ’upanddown’ pulses determined by an appropriate Poisson random measure. Processes are Hselfaffine (also frequently called ’selfsimilar’) ... 
Sample path properties of stochastic processes represented as multiple stable integrals
(ELSEVIER INC, 19910401)This paper studies the sample path properties of stochastic processes represented by multiple symmetric αstable integrals. It relates the “smoothness” of the sample paths to the “smoothness” of the (nonrandom) integrand. ... 
Weak convergence of sums of moving averages in the αstable domain of attraction
(INST MATHEMATICAL STATISTICS, 19920101)Skorohod has shown that the convergence of sums of i.i.d. random variables to an astable Levy motion, with 0 < a < 2, holds in the weakJ1 sense. J1 is the commonly used Skorohod topology. We show that for sums of moving ... 
The empirical process of some longrange dependent sequences with an application to Ustatistics
(Institute of Mathematical Statistics, 19891201)Let (Xj)∞ j = 1 be a stationary, meanzero Gaussian process with covariances r(k) = EXk + 1 X1 satisfying r(0) = 1 and r(k) = kDL(k) where D is small and L is slowly varying at infinity. Consider the twoparameter empirical ... 
Probability bounds for MSkorohod oscillations
(ELSEVIER SCIENCE BV, 19891001)Billingsley developed a widely used method for proving weak convergence with respect to the supnorm and J Skorohod topologies, once convergence of the finitedimensional distributions has been established. Billingsley's ...