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References
- 1
-
K. Aase.
A conditional expectation formula for diffusion processes.
J. Appl. Probab., 14:626-629, 1977.
- 2
-
M. Aizenman and B. Simon.
Brownian motion and Harnack inequality for Schrödinger
operators.
Comm. Pure Appl. Math., 35:209-273, 1982.
- 3
-
K. B. Athreya.
Darling and Kac revisted.
Sankya: The Indian Journal of Statistics, 48:255-266, 1986.
- 4
-
A. Benveniste and J. Jacod.
Systèmes de Lévy des processus de Markov.
Invent. Math., 21:183-198, 1973.
- 5
-
A. Berthier and B. Gaveau.
Critère de convergence des fonctionelles de Kac et applications
en mechanique et en géometrie.
J. Funct. Anal, 29:416-424, 1978.
- 6
-
J. Bertoin.
On the Hilbert transform of the local times of a Lévy
process.
Bull. Sci. Math., 119(2):147-156, 1995.
- 7
-
N. H. Bingham.
Limit theorems in fluctuation theory.
Advances in Appl. Prob., 5:554-569, 1973.
- 8
-
R. M. Blumenthal and R. K. Getoor.
Markov Processes and Potential Theory.
Academic Press, New York, 1968.
- 9
-
R. Carmona.
Regularity properties of Schrödinger and Dirichlet
semigroups.
J. Funct. Anal., 33(3):259-296, 1979.
- 10
-
K. L. Chung.
A probabilistic approach to the equilibrium problem in potential
theory.
Ann. Inst. Fourier, 23:313-322, 1973.
- 11
-
K. L. Chung and R. J. Williams.
Introduction to Stochastic Integration.
Birkhäuser-Verlag, 1990.
2nd edition.
- 12
-
Z. Ciesielski and S. J. Taylor.
First passage times and sojourn density for brownian motion in space
and the exact hausdorff measure of the sample path.
Trans. Amer. Math. Soc., 103:434-450, 1962.
- 13
-
D. A. Darling and M. Kac.
On occupation times for Markoff processes.
Trans. Amer. Math. Soc., 84:444-458, 1957.
- 14
-
R. Durrett.
Brownian motion and martingales in analysis.
Wadsworth, 1984.
- 15
-
E. B. Dynkin.
Infinitesimal operators of Markov processes.
Teor. Veroyatnost. i Primenen., 1:38-60, 1956.
- 16
-
E. B. Dynkin.
Markov Processes, I,II.
Springer, Berlin, Heidelberg, New York, Toronto, 1965.
(translated from the Russian edition of 1962).
- 17
-
E. B. Dynkin.
Local times and quantum fields.
In P. Huber and M. Rosenblatt, editors, Seminar on Stochastic
Processes, pages 69-84. Birkhäuser, 1983.
- 18
-
E. B. Dynkin.
Markov processes as a tool in field theory.
J. Funct. Anal., 50:167 - 187, 1983.
- 19
-
E. B. Dynkin.
Gaussian and non-Gaussian random fields associated with Markov
processes.
J. Funct. Anal., 55:344 - 376, 1984.
- 20
-
E. B. Dynkin.
Polynomials of the occupation field and related random fields.
J. Funct. Anal., 58:20 - 52, 1984.
- 21
-
R. J. Feynman.
Space-time approach to nonrelativistic quantum mechanics.
Rev. Mod. Phys., 20:367-387, 1948.
- 22
-
P. J. Fitzsimmons.
Harmonic morphisms and the resurrection of Markov processes.
In M. Barlow and N. Bingham, editors, Stochastic Analysis,
London Math. Soc. Lect. Note Series 167, pages 71-90. 1991.
- 23
-
P. J. Fitzsimmons and R. K. Getoor.
On the distribution of the Hilbert transform of the local time of a
symmetric Lévy process.
Ann. Probab., 20(3):1484-1497, 1992.
- 24
-
M. Fukushima, Y. Oshima, and M. Takeda.
Dirichlet forms and symmetric Markov processes, volume 19 of
de Gruyter Studies in Mathematics.
Walter de Gruyter & Co., Berlin, 1994.
- 25
-
R. K. Getoor and M. J. Sharpe.
Last exit decompositions and distributions.
Indiana Univ. Math. J., 23:377-404, 1973.
- 26
-
R. K. Getoor and M. J. Sharpe.
Last exit times and additive functionals.
Ann. Probab., 1:550 - 569, 1973.
- 27
-
J. Glover.
Energy and the maximum principle for nonsymmetric Hunt processes.
Theory Probab. Appl., 26:745 - 757, 1981.
- 28
-
J. Glover.
Representing last exit potentials as potentials of measures.
Z. Wahrsch. Verw. Gebiete, 61:17 - 30, 1982.
- 29
-
M. Iosifescu.
Finite Markov processes and their applications.
John Wiley & Sons (New York; Chichester), 1980.
- 30
-
K. Itô and H. P. McKean, Jr.
Diffusion Processes and their Sample Paths.
Springer, 1965.
- 31
-
M. Jeanblanc, J. Pitman, and M. Yor.
The Feynman-Kac formula and decomposition of Brownian paths.
Comput. Appl. Math., 16:27-52, 1997.
- 32
-
M. Kac.
On the distribution of certain Wiener functionals.
Trans. Amer. Math. Soc., 65:1-13, 1949.
- 33
-
M. Kac.
On some connections between probability theory and differential and
integral equations.
In J. Neyman, editor, Proc. Second Berkeley Symp. Math. Stat.
Prob., pages 189-215. Univ. of California Press, 1951.
- 34
-
I. Karatzas and S. Shreve.
Brownian Motion and Stochastic Calculus.
Springer-Verlag, 1988.
- 35
-
J. G. Kemeny and J. L. Snell.
Potentials for denumerable Markov chains.
J. Math. Anal. and Appl., 3:196-260, 1961.
- 36
-
J. T. Kent.
The appearance of a multivariate exponential distribution in sojurn
times for birth-death and diffusion processes.
In Probability, Statistics and Analysis, pages 161-179.
Cambridge Univ. Press, 1983.
London Math. Soc. Lecture Notes.
- 37
-
H. Kesten.
The influence of Mark Kac on probability theory.
Ann. Probab., 14:1103 - 1128, 1986.
- 38
-
R. Z. Khas'minskii.
On positive solutions of the equation au + vu = 0.
Theory Probab. Appl., 4:309-318, 1959.
- 39
-
J. F. C. Kingman.
Markov transition probabilities. IV: Recurrence time distributions
.
Z. Wahrsch. Verw. Gebiete, 11:9 - 17, 1968.
- 40
-
N. T. Longford.
Classes of multivariate exponential and multivariate geometric
distributions derived from Markov processes.
In A. R. Sampson H. W. Block and T. H. Savits, editors, Topics
in Statistical Dependence, volume 16 of Lecture Notes-Monograph
Series, pages 359-369. I. M. S., 1991.
- 41
-
M. B. Marcus and J. Rosen.
Moduli of continuity of local times of strongly symmetric Markov
processes via Gaussian processes.
J. Theoret. Probab., 5:791 - 825, 1992.
- 42
-
M. B. Marcus and J. Rosen.
p-variation of the local times of symmetric stable processes and
of Gaussian processes with stationary increments.
Ann. Probab., 20:1685 - 1713, 1992.
- 43
-
M. B. Marcus and J. Rosen.
Sample path properties of the local times of strongly symmetric
Markov processes via Gaussian processes.
Ann. Probab., 20:1603 - 1684, 1992.
- 44
-
M. B. Marcus and J. Rosen.
Logarithmic averages for the local times of recurrent random
walks and Lévy processes.
Stoch. Proc. Appl., 59:175-184, 1995.
- 45
-
M. B. Marcus and J. Rosen.
Gaussian chaos and sample path properties of additive
functionals of symmetric Markov processes.
Ann. Probab., 24:1130-1177, 1996.
- 46
-
P. A. Meyer.
Renaissance, recollements, mélanges, ralentissement de processus
de Markov.
Ann. Inst. Fourier Grenoble, 25:465-497, 1975.
- 47
-
P. A. Meyer, R. T. Smythe, and J. B. Walsh.
Birth and death of Markov processes.
In Proc. 6th Berk. Symp. Math. Stat. Prob., volume 3, pages
295-305, 1972.
- 48
-
T. Nagylaki.
The moments of stochastic integrals and the distribution of sojourn
times.
Proc. Nat. Acad. Sci. USA, 71:746-749, 1974.
- 49
-
R. Pinsky.
A spectral criterion for the finiteness or infiniteness of stopped
Feynman-Kac functionals of diffusion processes.
Ann. Probab., 14:1180 - 1187, 1986.
- 50
-
J. Pitman.
An identity for stopping times of a Markov process.
In Studies in Probability and Statistics, pages 41-57.
Jerusalem Academic Press, 1974.
- 51
-
J. Pitman.
Occupation measures for Markov chains.
Advances in Applied Probability, 9:69-86, 1977.
- 52
-
J. Pitman.
Lévy systems and path decompositions.
In Seminar on Stochastic Processes, 1981, pages 79-110.
Birkhäuser, Boston, 1981.
- 53
-
J. Pitman and M. Yor.
Moment generating functions for integrals of one-dimensional
diffusions.
In preparation, 1995.
- 54
-
P. S. Puri.
A method for studying the integral functionals of stochastic
processes with applications. II: Sojourn time distributions for Markov
chains.
Z. Wahrsch. Verw. Gebiete, 23:85 - 96, 1972.
- 55
-
D. B. Ray.
Sojourn times of a diffusion process.
Ill. J. Math., 7:615-630, 1963.
- 56
-
L. C. G. Rogers and D. Williams.
Diffusions, Markov Processes and Martingales, Vol. II: Itô
Calculus.
Wiley, 1987.
- 57
-
L. C. G. Rogers and D. Williams.
Diffusions, Markov Processes and Martingales, Vol. I:
Foundations.
Wiley, 1994.
2nd. edition.
- 58
-
J. Rosen.
Second order limit laws for the local times of stable
processes.
Séminaire de Probabilités,
XXV,pp. 407-424, Lect. Notes in Math. 1485, Springer, Berlin,
1991.
- 59
-
M. J. Sharpe.
General theory of Markov processes.
Academic Press, New York, London, 1988.
- 60
-
M. J. Sharpe.
Killing times for Markov processes.
Z. Wahrsch. Verw. Gebiete, 58:223 - 230, 1981.
- 61
-
P. Sheppard.
On the Ray-Knight Markov property of local times.
Journal of the London Mathematical Society, 31:377-384, 1985.
- 62
-
B. Simon.
Functional integration and quantum physics, volume 86 of
Pure and applied mathematics.
Academic Press, New York, 1979.
- 63
-
B. Simon.
Schrödinger semigroups.
Bull. A. M. S., 7:447-526, 1982.
- 64
-
D. W. Stroock.
Probability Theory, an Analytic View.
Cambridge Univ. Press, 1993.
- 65
-
D. Williams.
On local time for Markov chains.
Bull. A. M. S., 73:432-433, 1967.
- 66
-
D. Williams.
Fictitious states, coupled laws and local time.
Z. Wahrsch. Verw. Gebiete, 11:288-310, 1969.
Patrick Fitzsimmons
Wed May 17 08:50:36 PDT 2000