zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Stochastic calculus with respect to Gaussian processes. (English) Zbl 1015.60047
The authors consider a family of Gaussian processes (B t ) t + of the form B t = 0 t K(t,s)dW s , where K is a deterministic kernel and (W t ) t + is a standard Wiener process. They construct a stochastic calculus with respect to such processes via the stochastic calculus of variations, using the anticipating Skorokhod integral operator with respect to (W t ) t + , which is denoted by δ. The stochastic integral of an adapted process u with respect to (B t ) t is defined to be δ(K * u), where K * is the adjoint of the operator with kernel K. Itô and Stratonovich change of variable formulas and Hölder regularity results are proved for indefinite integrals with respect to (B t ) t , for a wide class of deterministic (singular and regular) kernels K. The results apply in particular to fractional Brownian motion with Hurst parameter H(1/4,1/2).

60H05Stochastic integrals
60H07Stochastic calculus of variations and the Malliavin calculus
60G15Gaussian processes