Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong Approximation of Iterated Ito and Stratonovich Stochastic
  Integrals Based on Generalized Multiple Fourier Series. Application to
  Numerical Solution of Ito SDEs and Semilinear SPDEs   The book is devoted to the strong approximation of iterated stochastic
integrals (ISIs) in the context of numerical integration of Ito SDEs and
non-commutative semilinear SPDEs with nonlinear multiplicative trace class
noise. The presented monograph opens up a new direction in researching of ISIs.
For the first time we successfully use the generalized multiple Fourier series
converging in the sense of norm in the space $L_2([t, T]^k)$ for the expansion
and strong approximation of Ito ISIs of multiplicity $k,$ $k\in{\bf N}$
(Chapter 1). This result is adapted for Stratonovich ISIs of multiplicities 1
to 5 (Chapter 2) as well as for some other types of ISIs (Chapter 1). Theorem
on expansion of Stratonovich ISIs of multiplicity $k$ ($k\in{\bf N}$) based on
multiple Fourier-Legendre series as well as multiple trigonometric Fourier
series is proved under condition of convergence of trace series (Chapter 2).
The integration order replacement technique for the class of Ito ISIs has been
introduced (Chapter 3). This result is generalized for the class of ISIs with
respect to martingales. We derived the exact and approximate expressions for
the mean-square error of approximation of Ito ISIs of multiplicity $k$,
$k\in{\bf N}$ (Chapter 1). Furthermore, we provided a significant practical
material (Chapter 5) devoted to the expansions and approximations of specific
Ito and Stratonovich ISIs of multiplicities 1 to 6 from the Taylor-Ito and
Taylor-Stratonovich expansions (Chapter 4) using the system of Legendre
polynomials and the system of trigonometric functions. The methods formulated
in this book have been compared with some existing methods (Chapter 6). The
results of Chapter 1 were applied (Chapter 7) to the approximation of ISIs of
multiplicity $k,$ $k\in{\bf N}$ with respect to the $Q$-Wiener process.

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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: econ