Marcus versus Stratonovich for systems with jump noise

Journal of Physics A: Mathematical and Theoretical

Volumn , Issue 34, 2014, Pages

  Chechkin, Alexei ^a,b   Pavlyukevich, Ilya ^c  

^a KHARKOV INSTITUTE OF PHYSICS AND TECHNOLOGY   (Ukraine)

^b MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^c FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

It Stratonovich dilemma; jump noise; Marcus equation

Indexed keywords

EID: 84906509962     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/47/34/342001     Document Type: Article

References (56)

1. Gardiner C W 2004 Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer Series in Synergetics) 3rd edn (Berlin: Springer)
2. van Kampen N G 2007 Stochastic Processes in Physics and Chemistry 3rd edn (Amsterdam: North-Holland)
3. Risken H 1989 The Fokker-Planck Equation: Methods of Solutions and Applications 2nd edn (Berlin: Springer)
4. Horsthemke W and Lefever R 1984 Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology (Springer Series in Synergetics vol 15) (Berlin: Springer)
5. Itô K 1944 Proceedings of the Imperial Academy 20 519-24
6. Gikhman I I and Skorokhod A V 1979 The Theory of Stochastic Processes III (Berlin: Springer)
7. Cont R and Tankov P 2004 Financial Modelling with Jump Processes (Boca Raton, FL: Chapman & Hall/CRC)
8. Sethi S P and Lehoczky J P 1981 J. Econ. Dyn. Control 3 343-56
9. Turelli M 1977 Theoretical Population Biology 12 140-78
10. Stratonovich R L 1966 SIAM Journal on Control 4 362-71 (In Russian: Vestnik Moskov. Univ. Ser. I Math. Meh., 1, 1964, 2-12)
11. Wong E and Zakai M 1965 The Annals of Mathematical Statistics 36 1560-4
12. West B J, Bulsara A R, Lindenberg K, Seshadri V and Shuler K E 1979 Physica A 97 211-33
13. Bulsara A R, Lindenberg K, Seshadri V, Shuler K E and West B J 1979 Physica A 97 234-43
14. van Kampen N G 1981 J. Stat. Phys. 24 175-87
15. Kupferman R, Pavliotis G A and Stuart A M 2004 Phys. Rev. E 70 036120
16. Mannella R and McClintock P V E 2012 Fluctuation and Noise Letters 11 1240010
17. Kuroiwa T and Miyazaki K 2014 J. Phys. A: Math. Theor. 47 012001
18. Hänggi P 1980 Phys. Lett. A 78 304-6
19. Grigoriu M 1998 Probabilistic Engineering Mechanics 13 175-82
20. Blanter Y M and Büttiker M 2000 Phys. Rep. 336 1-166
21. Schoutens W 2003 Lévy Processes in Finance: Pricing Financial Derivatives (Wiley Series in Probability and Statistics) (Chichester: John Wiley & Sons)
22. Grigoriu M and Samorodnitsky G 2004 J. Phys. A: Math. Gen. 37 8913-28
23. Pawley J B 2006 Handbook of Biological Confocal Microscopy 3rd edn ed J B Pawley (Berlin: Springer) 20-42
24. Er G K, Zhu H T, Iu V P and Kou K P 2009 Nonlinear Dyn. 55 337-48
25. Germano G, Politi M, Scalas E and Schilling R L 2010 Communications in Nonlinear Science and Numerical Simulation 15 1583-8
26. Suweis S, Rinaldo A, van der Zee S E A T M, Daly E, Maritan A and Porporato A 2010 Geophys. Res. Lett. 37 L07404
27. Suweis S, Porporato A, Rinaldo A and Maritan A 2011 Phys. Rev. E 83 061119
28. Srokowski T 2010 Phys. Rev. E 81 051110
29. Marcus S I 1978 IEEE Trans. Inf. Theory 24 164-72
30. Marcus S I 1981 Stoch. 4 223-45
31. Kurtz T G, Pardoux É and Protter P 1995 Annales de lInstitut Henri Poincaré, section B 31 351-7 (www.numdam.org/item?id=AIHPB-1995-31-2-351-0)
32. Kunita H 2004 Real and Stochastic Analysis. New Perspectives (Trends in Mathematics) ed M M Rao (Boston: Birkhäuser) 305-73
33. Applebaum D 2009 Lévy Processes and Stochastic Calculus (Cambridge Studies in Advanced Mathematics vol 116) 2nd edn (Cambridge: Cambridge University Press)
34. Kanazawa K, Sagawa T and Hayakawa H 2012 Phys. Rev. Lett. 108 210601
35. Kanazawa K, Sagawa T and Hayakawa H 2013 Phys. Rev. E 87 052124
36. Li T, Min B and Wang Z 2013 J. Chem. Phys. 138 104118
37. Li T, Min B and Wang Z 2014 J. Chem. Phys. 140 099902
38. di Paola M and Falsone G 1993 Probabilistic Engineering Mechanics 8 197-208
39. di Paola M and Falsone G 1993 J. Appl. Mech. 60 141-8
40. Sun X, Duan J and Li X 2013 Probabilistic Engineering Mechanics 32 1-4
41. Li T, Min B and Wang Z 2014 Phys. Rev. E 89 022144
42. Kloeden P E and Platen E 1995 Numerical Solution of Stochastic Differential Equations (Berlin: Springer)
43. Protter P E 2004 Stochastic Integration and Differential Equations (Applications of Mathematics vol 21) 2nd edn (Berlin: Springer)
44. Arnold L 1974 Stochastic Differential Equations: Theory and Applications (New York: Wiley-Interscience)
45. Kubo R 1963 J. Math. Phys. 4 174-83
46. Kunita H 1995 Stochastic Analysis (AMS) ed M C Cranston and M A Pinsky 323-41 (Providence, RI: AMS)
47. Tikhonov V and Mironov M 1977 Markov Processes. (Markovskie Protsessy) (Moskva: Sovetskoe Radio)
48. Hänggi P 1978 Helv. Phys. Acta 51 183-201
49. Hänggi P 1980 Helv. Phys. Acta 53 491-6
50. Klimontovich Y L 1990 Phys. A 193 515-32
51. Klimontovich Y L 1994 Phys.-Usp. 37 737-67
52. Dunkel J and Hänggi P 2005 Phys. Rev. E 72 036106
53. Yuan R and Ao P 2012 J. Stat. Mech. P07010
54. Shi J, Chen T, Yuan R, Yuan B and Ao P 2012 J. Stat. Phys. 148 579-90
55. Lau A W C and Lubensky T C 2007 Phys. Rev. E 76 011123
56. Sokolov I M 2010 Chem. Phys. 375 359-63