Publications of Fima Klebaner 
Books
2.  INTRODUCTION TO STOCHASTIC CALCULUS WITH APPLICATIONS. SECOND EDITION (revised and expanded)
Imperial College Press,  2005, 432pp. ISBN 1-86094-555-4 (Hardcover). Paperback ISBN 1-86094-566-X
SLIDES OF LECTURES AVAILABLE for instructors and lecturers (email me)

CORRECTIONS

1. INTRODUCTION TO STOCHASTIC CALCULUS WITH APPLICATIONS. 
Imperial College Press, 1998, 336pp. ISBN 1-86094-129-X    (reprinted 1999, 2001, 2004)   
 Books are distributed by WORLD SCIENTIFIC



  Book Chapters

 Discrete-Time Dynamical Systems as Population Models. In: Branching Processes:
Variation, Growth, and Extinction of Populations, Haccou P, Jagers P & Vatutin VA, pp. 88-94. Cambridge
University Press, 2005.  
Population Size Dependent Processes. In: Branching Processes: Variation, Growth,
and Extinction of Populations, Haccou P, Jagers P & Vatutin VA, pp. 133-135. Cambridge University Press, 2005.
Slowly Growing Populations. In: Branching Processes: Variation, Growth, and
Extinction of Populations, Haccou P, Jagers P & Vatutin VA, pp. 174-176. Cambridge University Press, 2005.

Important paper on Stochastic Implied Volatility Market Model

Publications in Refereed Journals


64. On the implicit Black-Scholes formula. (with Hamza K.) Stochastics: An International Journal of Probability and Stochastics Processes,   80 (2008),   No 1, 97-102.
63. Prediction of missing observations by control method (with Abramov V.). Advances and Applications in Statistics  8 (2008), 109-129.
62. Transformations of Galton-Watson processes and linear fractional reproduction (with U. Roesler and S. Sagitov) . Advances in  Applied Probability  39, 4, (2007), 1-18.
61. On One Inverse Problem in Financial Mathematics (with Hamza K.)  Journal of Uncertain Systems  (2007) vol.1, no.4, 258-267,   www.jus.org.uk
60. A family of non-Gaussian martingales with Gaussian marginals (with Hamza K.). Journal of Applied Mathematics and Stochastic Analysis (2007), Article ID 92723, 19 p.,  DOI 10.1155/2007/92723
59. Estimation and prediction of a non-constant volatility (with Abramov V.). Asia Pacific Financial Markets. (2007) 14, 1-23.
58. Large Deviations analysis of extinction in branching models (with Liptser R.). Mathematical Populations Studies. In Press.
57. Option pricing for log-symmetric distributions of returns (with Landsman Z.) Methodology and Computing in Applied Probability (2007) Springer. DOI 10.10007/s11009-007-9038-2
56. Cramer's theorem for nonnegative multivariate point processes with independent increments. (with Liptser R.)  Topics in Stochastic Analysis and  Nonparametric Estimation, IMA Volume 145 (2007), 21-28.
55. Markovian Paths to Extinction. (with Jagers P. and Sagitov S.) Advances in  Applied Probability  39 (2007), 569-587.
54. FCLT and MDP for stochastic Lotka-Volterra model. (with Lim A. and Liptser R.) Acta Applicandae Mathematicae. 97 (2007), no 1-3, 53-68.
53. On the path to Extinction. (with Jagers P. and Sagitov S.) Proceedings of the National Academy of Sciences. PNAS  ( 2007) vol.104, no15,  6107-6111
52.  On nonexistence of non-constant volatility in the Black-Scholes formula. (with Hamza K.)  Discrete and Continuous Dynamical Systems,  6 (2006),  829-834
51. Random volatility and option prices with the Generalized Student-t distribution. (with Fielding M.,  and Landsman Z.)   Advances and Applications in Statistics. 6 (2006), 111-120.
50. On Estimation of Volatility Surface and Prediction of Future Spot Volatility. (with Le T., Liptser R. ) Applied Mathematical Finance.  13(2006), No 3, 245-263
49.  Likely path to extinction in simple branching models with large initial population (with Liptser R.)  Journal of Applied Mathematics and Stochastic Analysis, 2006), Article ID 60376, 1-23.
48. On solutions of  first order stochastic partial differential equations.  (with Hamza K.) Far East J. Theo. Stat. 20 No. 1 (2006),    13 - 25.
47. Tracking volatility. (with Goldentyer L. and Liptser R.) Problems of Information Transmission  41 (2005), no 3, 32-50.
46. Behaviour of a dynamical system far from its equilibrium. Complex Analysis And Dynamical Systems II, 229-231. Contemp. Math., 382, Amer. Math. Soc., Providence, RI, 2005.
45. The EMM conditions in a general model for interest rates  (with Hamza K and Jacka S.D.)  Adv. Appl. Probab. 37 (2005), 415-434.
44. Branching processes in near-critical random enviroments. (with Jagers, P.) J. Appl. Probab. 41A (2004), 17--23.
43. Random variation and concentration effects in PCR. (with Jagers, P.) J. Theor. Biology  224/3 (2003), 299-304 
42. A Note on Averaging and Homogenization (with R. Khasminskii R.Z.) Stochastics and Dynamics, Vol. 3, No. 1 (2003) 113-120. 
41. Random Step Functions Model for Interest Rates (with Borovkov K. and Virag E.) Finance and Stochastics 7 (2003) , 123-143.
40. Some results on the Lotka-Volterra model and its small random perturbations. (with Khaminskii, R. Z. and Liptser, R.) Acta Applicandae Mathematicae 78 (2003), no. 1-3, 201--206.
39. Option price when the stock is a semimartingale. Elec. Comm. in Prob. 7 (2002), 89-93.  Correction Vol. 8 (2003),  C1-1.
38. The age of a Galton-Watson population with a geometric offspring distribution. (with S. Sagitov) J.  Appl. Probab. 39 (2002), 4, 816 -828.
37. Asymptotic analysis and extinction in randomly perturbed Lotka-Volterra model. (with Liptser R.) Annals of Applied Probability 11 (2001), 4, 1263-1291.
36. Long term behaviour of solutions of the Lotka-Volterra system under small random perturbations (with Khasminskii R.Z.) Annals of Applied Probability  11 (2001), 3, 952-963.
35. Population-Size-Dependent and Age-Dependent Branching Processes (with Jagers P.) Stochastic Processes and  Their Applications 87(2000), 235-254.
34. Moderate Deviations for Randomly Perturbed Dynamical Systems (with Liptser R.) Stochastic Processes and  Their Applications 80(1999), 157-176.
33. On the quasi-stationary distribution of some randomly perturbed transformations of the interval. (with Lazar, J. and Zeitouni, O.) Annals of Applied Probability. 8 (1998), no. 1, 300-315.
32. The Riemann's function and its application to stochastic perturbations of a non-linear wave equation. (with Bezen A.) Random & Computational Dynamics. 5 (1997), 307-318.
31. Galton-Watson Process (Update). Encyclopedia of Statistical Sciences, Update Vol. 1. S. Kotz Ed. (1997)Wiley, 252-256.
30. Stationary solutions and stability of second order random differential equations. (with Bezen A.) Physica A: Statistical and Theoretical Physics, 233/3-4 (1996), 809-823.
28. Large deviations for past dependent recursions. (with Liptser R.) Problems of Information Transmition. 32 (1996), 541-547.
27. Population and density dependent branching process. In Classical and Modern Branching Processes, Athreya K.B. and Jagers P. eds, Mathematics and Its Applications, IMA vol. 84 (1997), 165-170.
26. Conditions for integrability of Markov chains. (with Hamza K.) Journal of Applied Probability. 32 (1995), 541-547.
25. Sharp conditions for non explosions and explosions in Markov jump processes. (with Kersting G.) Annals of Probability. 23 (1995), 268-272.
24. The exit problem for a class of density dependent branching systems. (with Zeitouni O.) Annals of Applied Probability. 4 (1994), 1188-1205.
23. Representation of Markov chains as stochastic differential equations. (with Hamza K.) Lecture Notes in Statistics 99, (1995), Springer. C.C. Heyde (Ed.) Branching Processes: Proceedings of the First World Congress, 144-151.
22. Population dependent branching and iteration of maps. Probability Theory and Mathematical Statistics(1994), B. Grigelionis et al. (Eds). VSP/TEV, 391-399.
21. Asymptotic behaviour of Markov population processes with asymptotically linear rate of change. Journal of Applied Probability 31 (1994), No 3, 614-625.
20. Autoregressive ap proximation in Population-dependent branching processes with a threshold. (with Nerman O.) Stochastic Processes and Their Applications 51 (1994), No 1, 1-7.
19. Population-dependent branching processes with a threshold. Stochastic Processes and Their Applications 46 (1993), 115-127.
18. Asymptotic behaviour of near-critical population size dependent multitype Galton-Watson processes. Journal of Applied Probability 28 (1991), 512-519; Addendum. Journal of Applied Probability 29 (1992), 246.
17. Total life in a renewal process. Int. J. Math. Educ. Sci. Technol. (1991), 22, no. 1, 152-154.
16. Expected number of excursions above curved boundaries by a random walk. Bull. Austral. Math. Soc. 41 (1990), no. 2, 207--213.
15. Conditions for the unlimetted growth in multitype population size dependent Galton-Watson processes. Bull. Math. Biology (1990), 527-534.
14. Geometric growth in near-supercritical population size dependent multitype Galton-Watson processes. Ann. Probab. 17 (1989), no. 4, 1466--1477.
13. Stochastic difference equations and generalized gamma distributions. Ann. Probab. 17 (1989), no. 1, 178--188.
12. Linear growth in near-critical population-size-dependent multitype Galton-Watson processes. J. Appl. Probab. 26 (1989), no. 3, 431--445.
11. The volumes of simplices, or, find the penguin. J. Austral. Math. Soc. Ser. A 47 (1989), no. 2, 263--268.
10. The unemployment rate when the labour market is modelled by a Markov chain. Austral. J. Statist. 30 (1988), no. 2, 183--188.
9. Conditions for fixation of an allele in the density-dependent Wright-Fisher models. J. Appl. Probab. 25 (1988), no. 2, 247--256.
8. Geometric rate of growth in Markov chains with applications to population-size-dependent models with dependent offspring. (with Cohn, H). Stochastic Anal. Appl. 4 (1986), no. 3, 283--307.
7. On the renewal measure for Gaussian sequences. Statist. Probab. Lett. 4 (1986), no. 4, 167--171.
6. A limit theorem for population-size-dependent branching processes. J. Appl. Probab. 22 (1985), no. 1, 48--57.
5. On population-size-dependent branching processes. Adv. in Appl. Probab. 16 (1984), no. 1, 30--55.
4. Geometric rate of growth in population-size-dependent branching processes. J. Appl. Probab. 21 (1984), no. 1, 40--49.
3. Population-size-dependent branching process with linear rate of growth. J. Appl. Probab. 20 (1983), no. 2, 242--250.
2. A connection between the limit and the maximum random variable of a branching process in varying environments. (with Schuh H-J). J. Appl. Probab. 19 (1982), no. 3, 681--684.
1. Branching random walk in varying environments. Adv. in Appl. Probab. 14 (1982), no. 2, 359--367.
Research Reports in Mathematical Finance
 Multinomial pricing (with Hamza K.)  Report no 5, 1990
Extreme value estimators of volatility in stocks, Report no 4, 1991
Pricing of contingent claims on portfolios of assets (with Hamza K.) Report no 3, 1992
The Australian evidence for the universal portfolio (with Kalev P.), Report no 5, 1994