Journal Menu
Volume 11, Issue 1 (2019), Pages [1] - [87]
NEW FORWARD EQUATION FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH MULTIPLICATIVE NOISE
[1] L. Arnold, Stochastische Differentialgleichungen (Oldenbourg, München, 1973), and Stochastic Differential Equations: Theory and Applications, Wiley,
[2] I. I. Gichman and A. W. Skorochod, Stochastische Differentialgleichungen, Akademie-Verlag, Berlin, 1971.
[3] B. Oksendal, Stochastic Differential Equations, Springer,
[4] C. W. Gardiner, Handbook of Stochastic Methods, Springer,
[5] H. Risken, The Fokker-Planck Equation, 2nd Edition, Springer,
[6] D. Ryter, The Intrinsic “Sense” of Stochastic Differential Equations, arXiv.org/1605.02897.
[7] N. G. van Kampen, Stochastic Processes in Physics and Chemistry, 3rd Edition, Elsevier/North-Holland,
[8] D. Ryter and U. Deker, Properties of the noise-induced ‘‘spurious’’ drift, I, Journal of Mathematical Physics 21(11) (1980); Article 2662.
DOI: https://doi.org/10.1063/1.524381
[9] S. R. De Groot and P. Mazur, Non-Equilibrium Thermodynamics, North-Holland,
[10] D. Ryter, Stochastic differential equations: Loss of the Markov property by multiplicative noise, arXiv.org/1606.07464.
[11] D. Ludwig, Persistence of dynamical systems under random perturbations, SIAM Review 17(4) (1975), 605-640.
DOI: https://doi.org/10.1137/1017070
[12] D. Ryter, The exit problem at weak noise, the two-variable quasipotential, and the Kramers problem, Journal of Statistical Physics 149(6) (2012), 1069-1085.
DOI: https://doi.org/10.1007/s10955-012-0646-z
[13] Jianghong Shi, Tianqi Chen, Ruoshi Yuan, Bo Yuan and Ping Ao, Relation of a new interpretation of stochastic differential equations to Ito process, Journal of Statistical Physics 148(3) (2012), 579-590.