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THIS FORMULA IS A PARTICULAR CASE (FOR k=4) OF THE THEOREM 5.1, WHICH WAS PUBLISHED FOR THE FIRST TIME BY DMITRIY F. KUZNETSOV IN THE BOOK (PAGE 236): KUZNETSOV D.F. NUMERICAL INTEGRATION OF STOCHASTIC DIFFERENTIAL EQUATIONS. 2 (IN RUSSIAN). 2006, 764 PAGES. S.-PETERSBURG: POLYTECHNICAL UNIVERSITY PRESS. ISBN: 5-7422-1191-0. ALSO THE THEOREM 5.1 IS PRESENTED IN PUBLICATIONS OF DMITRIY F. KUZNETSOV AFTER 2006, FOR EXAMPLE, IN THE MONOGRAPH (PAGE 252): KUZNETSOV D.F. STOCHASTIC DIFFERENTIAL EQUATIONS: THEORY AND PRACTICE OF NUMERICAL SOLUTION. WITH MATLAB PROGRAMS. 6-TH EDITION (IN RUSSIAN). ELECTRONIC JOURNAL "DIFFERENTIAL EQUATIONS AND CONTROL PROCESSES" (ISSN 1817-2172). N4. 2018. 1073 PAGES. S.-PETERSBURG: S.-PETERSBURG STATE UNIVERSITY. THE THEOREM 5.1 OPEN A NEW DIRECTION IN THE FIELD OF STRONG (MEAN-SQUARE) APPROXIMATION OF MULTIPLE ITO AND STRATONOVICH STOCHASTIC INTEGRALS (CASE OF MULTIDIMENTIONAL WIENER PROCESS), WHICH PLAYS THE KEY ROLE IN SOLVING OF THE PROBLEM OF NUMERICAL INTEGRATION OF ITO STOCHASTIC DIFFERENTIAL EQUATIONS. |