A formal approach to stochastic integration and differential equations

References

• Gelfand , I. N. and N. Ya , Valenkin . 1964 . Generalized Functions , N.Y : Academic Press .
   Google Scholar
• Ito , K. 1944 . The stochastic integral . Proc. Imperial Acad , 20 : 519 – 524 . Tokyo
   Google Scholar
• Lamperti , J. 1964 . A simple construction of certain diffusion processes . J. Math. Kyoto , 4 : 161 – 170 .
   Google Scholar
• Paley , R. E. A. C. , Wiener , N. and Zygmund , A. 1959 . A note on random functions . Math. Z , 37 : 647 – 668 .
   Google Scholar
• 1968 . Conditional Markov Processes and their Application to the Theory of Optimal Control , N.Y : American Elsevier .
   Google Scholar
• 1977 . An interpretation of stochastic differential equations as ordinary differential equations which depend on the sample point . Bui, A.M.S , 83 : 296 – 298 .
   Google Scholar
• Turelli , M. 1977 . Random environments and stochastic calculus . Theoretical Population Biology , 12 : 140 – 178 .
   PubMed Web of Science ®Google Scholar
• McKean , H. P. 1969 . Stochastic Integrals , N.Y : Academic Press .
   Google Scholar
• Wong , E. and Zakai , M. 1965 . On the convergence of ordinary integrals to stochastic integrals . Annals Math. Stat , 36 : 1560 – 1564 .
   Google Scholar
• Watanabe , S. 1967 . On square-integrable martingales . Nagoya Math J , 30 : 209 – 245 .
   Web of Science ®Google Scholar
• Doss , H. 1977 . Liens entre equations differentielles stochastiques et ordinaires . Ann. Inst. Henri Poincare , 13 : 99 – 125 .
   Google Scholar
• Davis , M. H. A. 1978 . “ Martingale integrals and stochastic calculus ” . In Communication Systems and Random Process Theory , Edited by: Skwirzynski , J. K. Holland : Sisthoff and Nordhoff .
   Google Scholar