參考文獻 |
[1] Aase, K. K. (1986a). New option pricing formulas when the stock market is a
combined continuous point process. Technical Report. No. 60. CCREMS, MIT,
Cambridge, MA.
[2] Aase, K. K. (1986b). Probabilistic solutions of option pricing and corporate
security valuation. Technical Report. No. 63. CCREMS, MIT, Cambridge, MA.
[3] Alili, L. and Chaumont L. (2001). A new fluctuation identity for L´evy processes
and some applications. Bernoulli. 7, 557-569.
[4] Alos, E. Mazet, O. and Nualart, D. (2000). Stochastic calculus with respect
to fractional Brownian motion with Hurst parameter less than 1/2. Stochastic
Process. Appl. 86, 121-139.
[5] Andersen, P. K. Borgan, O. Gill, R. D. and Keiding, N. (1993). Statistical
Methods on Counting Processes. Springer-Velag.
[6] Aven, T. and Jensen, U. (1999). Stochastic Models in Reliability. Springer.
[7] Bachelier, L. (1990). Theorie de la speculation. Ann Sci. Ecole Norm. Sup. 17,
20-86.
[8] Barndorff-Nielsen, O. E. (1988). Parametric Statistical Models and Likelihood.
Lecture Notes in Statistics 50, Springer-Verlag.
[9] Barndorff-Nielsen, O. E. and Sørensen, M. (1994). A review of some aspects of
asymptotic likelihood theory for stochastic processes. International Statistical
Review. 50, 145-159.
[10] Basawa, I. V. and Prabhu, N. U. (1994). Statistical inference in stochastic
processes. Journal of Statistical Planning and Inference. 39.
[11] Basawa, I. V. and Prakasa Rao, B. L. S. (1980). Statistical Inference for Stochastic
Processes. Academic Press, London.
[12] Beran, J. (1994). Statistical Methods for Long Memory Processes. Chapman and
Hall, London.
[13] Berger, J. O. and Wolpert, R. L. (1988). The Likelihood Principle. Lecture
Notes-Monograph Series, Volume 6, Institute of Mathematical Statistics.
[14] Bertoin, J. (1996). L´evy Processes. Laboratoire de Probabilit´es Universit´e Pierre
et Marie Curie.
[15] Billingsley, P. (1961). Statistical Inference for Markov Processes. University of
Chicago Press, Chicago.
[16] Bingham, N. H. (1975). Fluctuation theory in continuous time. Adv. Appl.
Probab. 7, 705-766.
[17] Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities.
Journal of Political Economy. 81, 637-659.
[18] Bodo, B. A., Thompson, M. E., and Unny, T. E. (1987). A review on stochastic
differential equations for applications in hydrology. Stochastic Hydrol. Hydraul.
1, 81-100.
[19] Bosq, D. (1998). Nonparametric Statistics for Stochastic Process. 2nd. ed., Lecture
Notes in Statistics 110, Springer.
[20] Brown, B. M. and Hewitt, J. T. (1975). Asymptotic likelihood theory for diffusion
processes. Journal of Applied Probability. 12, 228-238.
[21] Brown, R. (1827). A Brief Account of Microscopical Observations. London.
[22] Chaumont, L. (1996). Conditionings and path decompositions for L´evy processes.
Stochastic Process Appl. 64, 39-54.
[23] Cheridito, A. (2001). Mixed fractional Brownian motion. Bernoulli. 7, 913-934.
[24] Chow, Y. S. and Teicher, H. (1997). Probability Theory. 3rd. ed., Springer.
[25] Ciesielski, Z. (1961). Holder condition for realizations of Gaussian processes.
Trans. Amer. Math. Soc. 99, 403-413.
[26] Cinlar, E. (1975). Introduction to Stochastic Processes. Prentice Hall.
[27] Coutin, L. and Qian, Z. (2000). Stochastic differential equations for fractional
Brownian motions. C. R. Acad. Sci. Paris S´e. I Math. 331, 75-80.
[28] Cox, D. R. (1975). Partial likelihood. Biometrika. 62, 269-276.
[29] Cox, D. R. and Lewis, P. A. W. (1978). The Statistical Analysis of Series of
Events. Chapman and Hall.
[30] Dai, W. and Heyde, C. (1996). Itˆo’s formula with respect to fractional Brownian
motion and its application. J. Appl. Math. Stochastic Anal. 9, 439-448.
[31] Decreusefond, L. and ¨Ustunel, A. (1997) Stochastic analysis of the fractional
Brownian motion. Potential Anal. 10, 177-214.
[32] Dietz, H. M. (1989). Asymptotic Properties of Maximum Likelihood Estimators
in Diffusion Type Models, Part 1: General Statements. Preprint No. 228,
Humboldt-Universit¨at, Berlin.
[33] Doob, J. L. (1953). Stochastic Processes. New York Wiley.
[34] Durrett, R. (1999). Essentials of Stochastic Processes. Springer.
[35] Eberlein, E. (2001). Application of Generalized Hyperbolic L´evy Motions to
Finance. In L´evy Process: Theory and Applications. Birkh¨auser: Basel.
[36] Eberlein, E. and Raible, S. (1999). Term structure models driven by general
L´evy process. Math. Finance. 9, 31-53.
[37] Edwards, A. F. (1972). Likelihood. Cambridge, U.K.: Cambridge University
Press.
[38] Einstein, A. (1905). On the movement of small particles suspend in a stationary
liquid demanded by the molecular-kinetic theory of heat. Ann. Physik. 17.
[39] Evans, M., Fraser, D. A., and Monette, G. (1986). On principles and arguments
to Likelihood. Canadian Journal of Statistics. 14, 181-199.
[40] Feigin, P. (1976). Maximum likelihood estimation for stochastic processes−A
martingale approach. Advances in Applied Probability. 8, 712-736.
[41] Fleischmann, K. and Mueller, C. (1997). A super-Brownian motion with a locally
infinite catalytic mass. Probab. Theory Related Fields. 107, 325-357.
[42] Fleischmann, K. and Klenke, A. (1999). Smooth density field of catalytic super-
Brownian motion. Ann. Appl. Probab. 19, 198-318.
[43] Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival
Analysis. Wiley.
[44] Fristedt, E. (1974). Sample Functions of Stochastic Processes with Stationary,
Independent Increments. Advances in Probability. 3, 241-396. Dekker, New
York.
[45] Geyer, C. (1999). Likelihood inference for spatial point processes. in Stochastic
Geometry: Likelihood and Computation, eds. O. E. Barndorff-Nielsen, W. S.Kendall, and M. N. M. van Lieshout, London: Chapman and Hall/CRC, 79-
140.
[46] Gihman, I. I. and Skorohod, A. V. (1975). The Theory of Stochastic Processes
II. Springer, Berlin.
[47] Godambe, V. P. and Heyde, C. C. (1987). Quasi-likelihood and optimal estimation.
International Statistical Review. 55, 231-244.
[48] Grandell, J. (1997). Mixed Poisson Processes. Chapman and Hall.
[49] Grenander, U. (1981). Abstract Inference. Wiley.
[50] Guttorp, P. (1991). Statistical Inference for Branching Processes. Wiley.
[51] He, S. W., Wang, J. G., and Yan, J.A. (1992). Semimartingale Theory and
Stochastic Calculus. Science Press.
[52] Heyde, C. C. (1997). Quasi-Likelihood and its Application. Springer.
[53] Hogg and Craig (1995). Introduction to Mathematical Statistics. 5th ed. Prentice
Hall.
[54] Hutton, J. E. and Nelson, P. I. (1986). Quasi-likelihood estimation for semimartingales.
Stochastic Processes and their Applications. 22, 245-257.
[55] Itˆo, K. (1961). Lectures on Stochastic Processes. Tata Institute of Fundamental
Research. Springer, Berlin.
[56] Jacod, J and Shiryaev, A. N. (1987). Limit Theorems for Stochastic Processes.
Springer, Berlin.
[57] Jeanblanc, M., Pitman, J., and Yor, M. (2002). Self-similar processes with
independent increments associated with L´evy and Bessel processes. Stochastic
Processes and their Applications. 100, 223-231.
[58] Kao, E. P. C. (1997). An Introduction to Stochastic Processes. Duxbury Press.
[59] Karlin, S. (1967). A First Course in Stochastic Processes. Academic Press, New
York.
[60] Karlin, S. and Taylor, H. (1980). A Second Sourse in Stochastic Processes.
Academic Press, New York.
[61] Karr, A. F. (1991). Point Processes and their Statistical Inference. Marcel
Dekker, New York.
[62] Kingman, J. F. C. (1993). Poisson Processes. Oxford University Press.
[63] K¨uchler, U. (2004). On integrals with respect to L´evy processes. Statistics &
Probability Letters. 66, 145-151.
[64] K¨uchler, U. and Sørensen, M. (1997). Exponential Families of Stochastic Processes.
Springer.
[65] Kutoyants, Yu. A. (1984). Parameter Estimation for Stochastic Processes.
Translated and edited by Prakasa Rao, B. L. S. Heldermann, Verlag Berlin.
[66] Kutoyants, Yu. A. (2004). Statistical Inference for Ergodic Diffusion Processes.
Springer.
[67] LeBlanc, B. and Yor, M. (1998). L´evy Processes in finance: A remedy to the
non-stationarity of continuous martingales. Finance and Stochastics. 2, 399-408.
[68] Le´on, J. A., Sol´e, J. L., Utzet, F., and Vives, J. (2002). On L´evy processes,
Malliavin calculus and market models with jumps. Finance Stochast. 6, 197-
225.
[69] Leskow, J. and Rozanski, R. (1989). Maximum likelihood estimation of the drift
function for a diffusion process. Statistics and Decisions. 7, 243-262.
[70] L´evy, P. (1939). Sur certains processus stochastiques homogenes. Compositio
Math. 7, 283-339.
[71] L´evy, P. (1948). Processus Stochastiques et Mouvement Brownien. Gauthier-
Villars, Paris.
[72] L´evy, P. (1954). Th´eorie de L’addition des Variables Al´eatoires. 2nd edn.
Gauthier-Villars, Paris.
[73] Lin, S. (1995). Stochastic analysis of fractional Brownian motions. Stochastics
Stochastics Rep. 55, 121-140.
[74] Mandelbrot, B. B. and Van Ness, J. W. (1968). Fractional Brownian motions,
fractional noises and applications. SIAM Rev. 10, 422-437.
[75] Mazo, R. M. (2002). Brownian Motion. Clarendon Press. Oxford.
[76] McCullagh, P. (1983). Quasi-Likelihood Functions. Annals of Statistics. 11, 59-
67.
[77] Merton, R. C. (1973). Theory of rational option pricing. Bell Journal of Economics
and Management Science. 4, 141-183.
[78] Mikosch, T., Resnick, S., Rootzen, H. and Stegeman, A. (2002). Is network
traffic approximated by stable L´evy motion or fractional Brownian motion?.
The Annals of Applied Probability. 12, 23-68.
[79] Mishra, M. N. and Bishwal, J. P. N. (1995). Approximate maximum likelihood
estimation for diffusion processes from discrete observations. Stochastics and
Stochastics Reports. 52, 1-13.
[80] Mishra, M. N. and Prakasa Rao, B. L. S. (1985a). Asymptotic study of the
maximum likelihood estimator for nonhomogeneous diffusion processes. Statistics
and Decisions. 3, 193-203.
[81] Mishra, M. N. and Prakasa Rao, B. L. S. (1985b). On the Berry-Esseen bound
for maximum likelihood estimator for linear homogeneous diffusion processes.
Sankhy¯a A. 47, 392-398.
[82] Morales, M. and Schoutens, W. (2003). A risk model driven by L´evy processes.
Appl. Stochastic Models Bus. Ind. 19, 147-167.
[83] Mtundu, N. D. and Koch, R. W. (1987). A stochastic differential equation
approach to soil moisture. Stochastic Hydrol. Hydraul. 1, 101-116.
[84] Muisela, M. and Rutkowski, R. (1998). Martingale Methods in Financial Modeling.
Springer.
[85] Nualart, D. and Schoutens, W. (2000). Chaotic and predictable representation
for L´evy processes. Stochastic Process Appl. 90, 109-122.
[86] Owen, A. B. (2001). Empirical Likelihood. Chapman and Hall.
[87] Parzen, E. (1962). Stochastic Processes. Holden-Day.
[88] Pedersen, A. R. (1995). Consistency and asymptotic normality of an approximate
maximum likelihood estimator for discretely observed diffusion processes.
Bernoulli. 1, 257-279.
[89] Philippe, C., Laure, C. and G´erard M. (2003). Stochastic integration with respect
to fractional Brownian motion. Ann. I. H. Poincar´e-PR39. 1, 27-68.
[90] Pipiras, V. and Taqqu, M. S. (2000). Integration questions related to fractional
Brownian motion. Probab. Theory Related Fields. 251-291.
[91] Prabhu, N. U., ed. (1988). Statistical Inference from Stochastic Processes. (Contemporary
Mathematics, Vol. 80). American Mathematical Society, Providence,
RI.
[92] Prabhu, N. U. and Basawa, I. V. (1991). Statistical Inference in Stochastic
Processes. Marcel Dekker, New York.
[93] Prakasa Rao, B. L. S. (1972). Maximum likelihood estimation for Markov processes.
Annals of the Institute of Statistical Mathematics. 24, 333-345.
[94] Prakasa Rao, B. L. S. (1999a). Statistical Inference for Diffusion Type Process.
Arnold.
[95] Prakasa Rao, B. L. S. (1999b). Semimartingales and their Statistical Inference.
Chapman and Hall.
[96] Prakasa Rao, B. L. S. and Bhat, B. R. (1996). Stochastic Processes and Statistical
Inference. New Age International, New Delhi.
[97] Protter, P. (1990). Stochastic Integration and Differential Equations. Springer.
[98] Reid, N. (2000). Likelihood. Journal of the American Statistical Association.
95, 1335-1340.
[99] Ren, Y. (2001). Construction of super-Brownian motions. Stochastic Analysis
and Applications. 19, 103-114.
[100] Revuz, D. and You, M. (1994). Continuous Martingales and Brownian Motion.
Springer.
[101] Robins, J. and Wasserman, L. (2000). Conditioning, Likelihood, and Coherence:
A Review of Some Foundational Concepts. 95, 1340-1346.
[102] Rogers, L. C. G. (1997). Arbitrage with fractional Brownian motion. Math.
Finance. 7, 95-105.
[103] Rogers, L. C. G. and Williams, D. (1994). Diffusions Markov Processes, and
Martingales vol. I: Foundations. [1st ed. by Williams, D., 1979.] Wiley.
[104] Ross, S. M. (1997). Introduction to Probability Models. 6th. ed., Academic Press.
[105] Sato, K. (1990). Stochastic Processes with Stationary Independent Increments.
Kinokuniya, Tokyo.
[106] Sato, K. (1995). L´evy Processes on the Euclidean Spaces. University of Zurich.
[107] Sato, K. (1999). L´evy Processes and Infinitely Divisible Distributions. Cambridge
University Press.
[108] Schoutens, W. (2003). L´evy Processes in Finance: Pricing Financial Derivatives.
Wiley.
[109] Severini, T. A. (2000). Likelihood Methods in Statistics. Oxford Univ. Press.
[110] Shorack, G. and Wellner, J. A. (1986). Empirical Processes with Applications
to Statistics. Wiley, New York.
[111] Skorohod, A. V. (1991). Random Processes with Independent Increments.
Kluwer, Dordrecht, Netherlands.
[112] Sørensen, M. (1983). On maximum likelihood estimation in randomly stopped
diffusion-type processes. International Statistical Review. 51, 95-110.
[113] Stark, H. and Woods, J. W. (2002). Probability and Random Processes with
Applications to Signal Processing. 3rd. ed., Prentice Hall.
[114] Taniguchi, M. and Kakizawa, Y. (2000). Asymptotic Theory of Statistical Inference
for Time Series. Springer.
[115] Taylor, S. J. (1973). Sample path properties of processes with stationary independent
increments. Stochastic Analysis, 387-414. Wiley, London.
[116] Tsou, T. S. and Royall, R. M. (1995). Robust likelihood. JASA. 90, 316-320.
[117] Wang, Y. (2002). An alternative approach to super-Brownian motion with a
locally infinite branching mass. Stochastic Processes and Applications. 102, 221-
233.
[118] Welsh, A. H. (1996). Aspects of Statistical Inference. Wiley.
[119] Wiener, N. (1924). Un probl`eme de probabilit´es d´enombrables. Bull Soc. Math.
France. 52, 569-578.
[120] Wiener, R. (1923). Differential space. J. Math. Phys. 2, 131-174.
[121] Yor, M. (2001). Exponential Functionals of Brownian Motion and Related Processes.
Springer.
[122] Yoshimoto, A., Shoji, I. and Yoshimoto, Y. (1996). Application of a stochastic
control model to a free market policy of rice. Statistical Aalysis of Time Series.
Research Report No. 90, Institute of Statistical Mathematics. Tokyo. |