Areas of expertise

• Stochastic Analysis And Modelling 010406
• Statistics 0104

Research interests

Publications

• Buchmann, B & Muller, G 2021, 'Changing Structures at Electricity Markets: Modelling spot prices using time-varying stable CARMA models', Journal of Econometrics and Statistics, vol. 1, no. 2, pp. 121-133.
• Buchmann, B, Ferreira, A & Maller, R 2021, 'Convergence of extreme values of Poisson point processes at small times', Extremes, vol. 24, pp. 501-529.
• Buchmann, B, Lu, K & Madan, D 2019, 'Weak subordination of multivariate Lévy processes and variance generalised gamma convolutions', Bernoulli, 25, pp. 742-770.
• Buchmann, B, Lu, K & Madan, D 2020, 'Self-Decomposability of weak variance generalised gamma convolutions', Stochastic Processes and their Applications 1, pp. 630-655.
• Buchmann, B, Lu, K & Madan, D 2019, 'Calibration for Weak Variance-Alpha-Gamma Processes', Methodology and Computing in Applied Probability, 21, 1151--1164
• Buchmann, B, Maller, R & Resnick, S 2018, 'Processes of rth largest, Extremes, 21, 485–508.
• Buchmann, B, Ipsen, Y & Maller, R 2017, 'Functional laws for trimmed Levy processes', Advances in Applied Probability 54, 873–889.
• Buchmann, B, Kaehler, B, Maller, R, Szimayer, A. 2017, 'Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing', Stochastic Processes and their Applications 127, 2208--2242.
• Buchmann, B, Fan, Y. & Maller, R 2016 'Distributional Representations and Dominance of a Levy Process over its Maximal Jump Processes', Bernoulli, 22, 2325-2371.
• Buchmann, B, Maller, R & Mason, D 2015, 'Laws of the iterated logarithm for self-normalised Levy processes at zero', Transactions of the American Mathematical Society, 367, 1737-1770.
• Buchmann, B & Chan, N 2013, 'Unified asymptotic theory for nearly unstable AR(p) processes', Stochastic Processes and their Applications, vol. 123, no. 3, pp. 952-985.
• Buchmann, B & Müller, G 2012, 'Limit experiments of GARCH', Bernoulli, vol. 18, no. 1, pp. 64-99.
• Buchmann, B & Maller, R A 2011, 'The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component.' Probability Theory and Related Fields, vol. 149, no. 1-2, pp. 303--330.
• Buchmann, B & Chan, N H 2009, 'Integrated functionals of normal and fractional processes.' Annals of Applied Probability, vol. 19, no. 1, 49--70.
• Buchmann, B. 2009, 'Weighted empirical processes in the nonparametric inference for Lévy processes.' Mathematical Methods of Statistics, vol. 18, no. 4, pp. 281--309.
• Buchmann, B, Maller, R A & Szimayer, A 2008, 'An almost sure functional limit theorem at zero for a class of Lévy processes normed by the square root function, and applications.' Probability Theory and Related Fields, vol. 142, no. 1-2, pp. 219-247.
• Buchmann, B & Weber, S 2007, 'A continuous time approximation of an evolutionary stock market.', International Journal of Theoretical and Applied Finance, vol. 10, no. 7, pp. 1229--1253.
• Buchmann, B & Chan, N H 2007, 'Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence', Annals of Statistics, vol. 35, no. 5, pp. 2001-2017.
• Buchmann, B & Klüppelberg, C 2006, 'Fractional Integral Equations and State Space Transforms', Bernoulli, vol. 12, no. 3, pp. 431-456.
• Buchmann, B & Klüppelberg, C 2005, 'Maxima of stochastic processes driven by fractional Brownian motion', Advances in Applied Probability, vol. 37, no. 3, pp. 743-764.
• Buchmann, B & Klüppelberg, C 2004, 'Extremal Behaviour of Fractal Models', Statistics in Finance, ed. Richard Davis and Claudia Kluppelberg, Mathematisches Forschungsinstitut Oberwolfach, Germany, pp. 121-123.
• Buchmann, B & Grübel, R 2004, 'Decompounding Poisson random sums: recursively truncated estimates in the discrete case.' Annals of the Institute of Statistical Mathematics, vol. 56, no. 4, pp. 743-756.
• Buchmann, B & Grübel, R 2003, 'Decompounding: an estimation problem for Poisson random sums', Annals of Statistics, vol. 31, no. 4, pp. 1054-1074.

Projects and Grants

Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.

• Frontiers of Risk Modelling: Dependence and Extremes of Levy Processes (Primary Investigator)