Books and Editorships

 

1. E. Mayer-Wolf, E. Merzbach and A. Shwartz (eds.): Stochastic Analysis : A Liber Amicorum for Moshe Zakai, Academic Press, 1991, XX + 532 pp.

 

2. E. Merzbach and A. Shimron: Probability Theory, Hebrew, Akademon, 1993, 321 pp.; Augmented and revised second edition, 1994, 333 pp.; third edition, 1999, 335 pp.; fourth edition, 2003, 336 pp.

 

3. J.P. Fouque, K. Hochberg and E. Merzbach (eds.): Stochastic Analysis: Random Fields and Measure-Valued Processes, Israel Math. Conf. Proc., no. 10, 1996, 214 pp.

 

4. G. Ivanoff and E. Merzbach: Set-Indexed Martingales, Chapman & Hall / CRC, London, 2000, 212 pp.

 

5. E. Merzbach (ed.): Topics in Spatial Stochastic Processes, Springer-Verlag, Lecture Notes in Math., vol. 1802, 2003, 251 pp.

 

Papers

 

6. Stopping for two-dimensional stochastic processes, Stochastic Processes and their Applications 10, 49-63 (1980).

 

7. Une remarque sur les martingales à deux indices et leurs mesures de Doléans associées, C.R. Acad. Sci. Tome 290, 435-438 (1980).

 

8. Processus stochastiques à indices partiellement ordonnés, Publication Math. App., Ecole Polytechnique, 69 pp. (1980).

 

9. Predictable and dual predictable projections of two-parameter stochastic processes (with M. Zakai), Zeit. für Wahr. verw. Gebiete, 53, 263-269 (1980).

10. On Doob-Meyer decomposition, 4th International Conference of Collective Phenomena, Moscow, April 1980; Annals New York Acad. Sciences, 205-208 (1981).

 

11. Discontinuités de martingales à variation intégrable (with G. Mazziotto and J. Szpirglas), Lecture Notes in Math. 863, Springer-Verlag, 59-83 (1981).

 

12. Extension and continuity of the stochastic integral in the plane, Notes Sem. Proc. Aleatoires et Applic. Telecommunications, 5, 79-88 (1981).

 

13. Mathematical-educational implications of some statistical distribution problems (with S. Yeshurun), Int. J. Math. Educ. Sci. Technol., 14, 189-200 (1982).

 

14. Chemins croissants optionnels et théorème de section, Annals Inst. H. Poincaré, 3, 223-234 (1983).

 

15. Regularity and decomposition of two-parameter supermartingales (with G. Mazziotto), J. Multivariate Analysis, 17, 38-55 (1985).

 

16. Different kinds of two-parameter martingales (with D. Nualart), Israel J. of Math., 52, 193-208 (1985).

 

17. Bimeasures and measures induced by planar stochastic integrators (with M. Zakai), J. Multivariate Analysis 19, 67-87 (1986).

 

18. A characterization of the spatial Poisson process and changing time (with D. Nualart), Ann. of Probability, 13, 1380-1390 (1986).

 

19. Stopping a two-parameter weak martingale (with M. Zakai), Probability Theory and Related Fields (Z.W.) 76, 499-507 (1987).

 

20. Analyse non-standard à l'usage du probabiliste, Course at Ecole Polytechnique, 31 pp. (1987).

 

21. A martingale approach to point processes in the plane (with D. Nualart), Ann. of Probability, 16, 265-274 (1988).

 

22. Point processes indexed by directed sets (with G. Mazziotto), Stochastic Processes and their Applications, 30, 105-119 (1988).

 

23. Point processes in the plane, Acta Applicandae Mathematicae, 12, 79-101 (1988).

24. Generalized holomorphic processes and differentiability (with D. Nualart), J. Theor. Probab., 2, 419-432 (1989).

 

25. Markov properties for point processes on the plane (with D. Nualart), Ann. of Probability, 18, 342-358 (1990).

 

26. Characterization of compensators for point processes on the plane (with G. Ivanoff), Stochastics 29, 395-405 (1990).

 

27. On the extension of bimeasures (with S. Karni), Journal d'Analyse Mathématique, 55, 1-16 (1990).

 

28. Intensity-based inference for point processes (with G. Ivanoff), Journal of Multivariate Analysis 32, 269-281 (1990).

 

29. Orderliness and compensation for multi-parameter point processes, Probab. and Math. Statistics, 12, 255-264 (1991).

 

30. Set-indexed stochastic processes and predictability (with G. Ivanoff), Theor. Probab. Applic., 37, 57-63 (in Russian) (1992), English translation: 37, 61-66 (1992).

 

31. Worthy martingales and integrators (with M. Zakai), Statistics and Probability Letters, 16, 391-395 (1993).

 

32. Predictability and stopping on lattices of sets (with G. Ivanoff and I. Schiopu-Kratina), Probab. Th. and Rel. Fields, 97, 433-446 (1993).

 

33. A limit theorem for linear boundary value problems in random media (with J.P. Fouque), Ann. of Appl. Probability, 4, 549-569 (1994).

 

34. Doob-Meyer decomposition for set-indexed submartingales (with M. Dozzi and G. Ivanoff), J. Theor. Probab., 7, 499-525 (1994).

 

35. A martingale characterization of the set-indexed Poisson process (with G. Ivanoff), Stochastics, 51, 69-82 (1994).

 

36. How to construct a partition given preference sets (with B. Singer), Comp. & Oper. Research, 21, 1061-1068 (1994).

 

37. Lattices of Random sets and Progressivity (with G. Ivanoff and I. Schiopu-Kratina), Stat. and Probab. Letters, 22, 97-102 (1995).

 

38. Weak convergence of Markov processes using projective systems (with B. Singer), Bull. Sc. Math., 119, 129-145 (1995).

 

39. Stopping and set-indexed local martingales (with G. Ivanoff), Stoch. Proc. and their Applic., 57, 83-98 (1995).

 

40. Multi-parameter stochastic processes via non-standard analysis (with L. Manevitz), Israel Math. Conf. Proc., vol. 10, 150-167 (1996).

 

41. Weak convergence for set-indexed point processes and the Poisson process (with G. Ivanoff and Y. Lin), Th. of Probab. and Math. Stat., 55, 77-89 (1996).

 

42. A martingale characterization of the set-indexed Brownian motion (with G. Ivanoff), J. Theor. Probab., 9, 903-913 (1996).

 

43. A note on expansion for functionals of spatial marked point processes (with B. Blaszczyszyn and V. Schmidt), Stat. and Probab. Letters, 36, 299-306 (1997).

 

44. Poisson convergence for set-indexed empirical processes (with G. Ivanoff), Stat. and Probab. Letters, 32, 81-86 (1997).

 

45. Asymptotic results for mixing random ordinary differential equations (with B. Lukacher), Functional Differential Equations, 4, 111-124 (1997).

 

46. Set-indexed Markov processes (with G. Ivanoff), Canadian Math. Soc. Conf. Proc. 26, 217-232 (2000).

 

47. A Skorokhod topology for a class of set-indexed functions, (with G. Ivanoff), in: Skorokhods Ideas in Probability Theory, National Academy of Sciences of Ukraine,Kiev, 172-178 (2000).

 

48. Stochastic integration for set-indexed processes (with D. Saada), Israel J. of Math. 118, 157-181 (2000).

 

49. Limit theorems for sums of random fuzzy sets (with D. Dozzi and V. Schmidt), Journal Mathematical Analysis and Applic. 259, 554-565 (2001).

 

50. Random censoring in set-indexed survival analysis (with G. Ivanoff), Ann. of Applied Probab. 12, 944-971 (2002).

 

51. The set-indexed bandit problem (with G. Aletti), Stoch. Proc. and their Applic. 101, 127-142 (2002).

 

52. Central limit theorems for the ergodic adding machine (with M. Levin), Israel J. Math. 134, 61-92 (2003).

 

53. An introduction to the general theory of set indexed martingales, in: Topics in Spatial Stochastic Processes, Lecture Notes in Math., vol. 1802, 41-84, Springer-Verlag, 2003.

 

54. Random clouds and an application to censoring in survival analysis (with G. Ivanoff), Stoch. Proc. and their Applic. 111, 259-279 (2004).

 

55. Stopping Markov processes and first path on graphs (with G. Aletti), Journal Eur. Math. Soc. 8, 49-75 (2006).

56. A set-indexed fractional Brownian motion (with E. Herbin), J. Theor. Probab. 19, 337-364 (2006).

 

57. The multiparameter fractional Brownian motion (with E. Herbin), in: "Math Everywhere," Proc. VK60, 92-101, Springer, 2006.

 

58. What is a multi-parameter renewal process? (with G. Ivanoff), Stochastics 78, 411-441 (2006).

 

59. A characterization of the set-indexed fractional Brownian motion by increasing paths (with E. Herbin), C.R. Acad. Sci. Paris, Ser. I, 343, 767-772, 2006.

 

60. A compensator characterization of point processes on toplogical lattices (with G. Ivanoff and M. Plante), Electron. J. of Probability 12, 47-74 (2007).

 

61. Characterizations of multiparameter Cox and Poisson processes by the renewal property (with Y. Shaki), Stat. Probab. Letters 78, 637-642 (2008).

 

62. Stationarity and self-similarity characterization of the set-indexed fractional Brownian motion (with E. Herbin), J. Theor. Probab. 22, 1010-1029 (2009).

 

63. Set-indexed Brownian motion on increasing paths (with A. Yosef), J. Theor. Probab. 22, 883-890 (2009).

 

64. Multi-step "word-of-mouth" communication influence in marketing: A mathematical model (with J. Picard), Int. J. Pure Applied Math. 54, 503-519 (2009).

 

65. Optimal detection of a change-set in a spatial Poisson process (with G. Ivanoff), Ann. of Applied Probab. 20, 640-659 (2010).

 

66. A non-contagious random spread of marketing messages (with J. Picard), Int. J. Pure Applied Math. 79, 505-519 (2012).

 

67. The set-indexed Lévy process (with E. Herbin), submitted.

 

68. Fractional Poisson random fields (with N. Leonenko), in preparation

 

Note: In all the joint papers the authors are listed alphabetically.

 

 

Related Publications and Related Editorships (in Hebrew, except no.1)

 

1. D. et l'infini mathematique, Koumi 20, 10-19 (1977).

 

2. Random processes in Rabbinic thought, Higayon, vol. 1, 31-38 (1989).

 

3. M. Koppel and E. Merzbach (eds.): Higayon, Studies in Rabbinic Logic, Aluma Press, Jerusalem, Vol. 1, 1989; Vol. 2, 1992; vol. 3, 1995; vol. 4, 1997, Vol. 5, 2001.

 

4. The nearest town in the matter of "Egla Arufa" (with B. Singer), Higayon, vol. 2, 76-84 (1992).

 

5. On the definition of the area of a rectangle (1994).

 

6. M. Koppel and E. Merzbach (eds.): Sefer Higayon, Aluma Press, Jerusalem (1995).

 

7. The case of the intermingled babies: probabilistic and psychologic perspectives (with R. Miller), Higayon, vol. 3, 155-160 (1995).

 

8. On the accidental and randomness, Higayon, vol. 3, 48-51 (1995).

 

9. A short history of the theory of probability, Aleh 17, Hebrew University, Jerusalem, 15-19, (1995).

 

10. Statistics and the hidden blessings, BaDaD. vol. 2, 5-10 (1996).

 

11. To pray for success in a lottery, (with N. Taylor), Tehumin, 16, 443-448 (1996).

 

12. Following the lottery, you will share, Aleph Zero 5, 16-18 (1996).

 

13. The lottery in the world of prayer, (with N. Taylor), Higayon, vol. 4, 105-112 (1997).

14. About "Free numbers", Aleh, 21, Hebrew University, Jerusalem, 7-12 (1997).

 

15. Rains, blessings and traffic accidents (1997).

 

16. The census of Israel in the Torah, Higayon, vol. 5, 97-104 (2001); abridged version in: Weakly Torah Readings, no. 238 Bar-Ilan University (2000).

 

17. The middle of the Torah in words, Weakly Torah Readings, no. 334, Bar-Ilan University (2000).

 

18. Mixing of sacrifices, Matematika BaHamad, no.9, 16-18 (2000).

 

19. The attempts at changing the weekly calendar and the Jewish Sabbath, BaDaD., vol. 12, 61-70 (2001).

 

20. Verses in the Bible containing all the letters of the Hebrew alphabet, Weakly Torah Readings, no. 404, Bar-Ilan University (2001).

 

21. Moshe and the 7th of Adar, Weakly Torah Readings, no. 433, Bar-Ilan University (2002).

 

22. Management of nations following Torah principles, 100 Years in Religious Zionism, S. Raz (ed.), 140-145 (2002).

 

23. The lengths of the names of the men, Weekly Torah Readings, no. 552, Bar-Ilan University (2004).

 

24. Using the Goral to determine legal and Halachic decisions, Tehumin 24, 460-464 (2004).

 

25. On the seventy elders, Weekly Torah Readings, no. 656, Bar-Ilan University (2006).

 

26. Drawing of lots in the Yom Kippur service, for what purpose?, Weekly Torah Readings, no. 701, Bar-Ilan University (2007).

 

27. Moving Pesach towards the summer, BaDaD 18, 99-105 (2007).

 

28. The Logic of the Lottery, (book), Reuven Mass, Ltd. (2009), 208pp.

 

29. Randomness and the hidden Divine presence in the world, to appear.

 

30. On the "three times 'Hazaqa'" (with Y. Heshkovitz), to appear in Yeshurun.

 

31. An abridged history of astronomy, 2009.