Expansion of Iterated Stratonovich Stochastic Integrals of Fifth Multiplicity Based on Generalized Multiple Fourier Series
Abstract
The article is devoted to the construction of expansion of iterated Stratonovich stochastic integrals of fifth multiplicity based on the method of generalized multiple Fourier series converging in the sense of norm in Hilbert space $L_2([t, T]^k),$ $k\in\mathbb{N}.$ The mentioned expansion converges in the meansquare sense and contains only one operation of the limit transition in contrast to its existing analogues. The expansion of iterated Stratonovich stochastic integrals turned out much simpler than the appropriate expansion of iterated Ito stochastic integrals. We use the expansion of the latter as a tool of the proof of the expansion for iterated Stratonovich stochastic integrals. The iterated Stratonovich stochastic integrals are the part of the TaylorStratonovich expansion of solutions of Ito stochastic differential equations. That is why the results of the article can be applied to the numerical integrations of Ito stochastic differential equations.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.00643
 Bibcode:
 2018arXiv180200643K
 Keywords:

 Mathematics  Probability
 EPrint:
 38 pages. Minor changes. arXiv admin note: substantial text overlap with arXiv:1801.01564, arXiv:1801.05654, arXiv:1712.09516