dimension

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di·men·sion

(di-men'shŭn),
Scope, size, magnitude; denoting, in the plural, linear measurements of length, width, and height.

di·men·sion

(di-men'shŭn)
Scope, size, magnitude; denoting, in the plural, linear measurements of length, width, and height.

di·men·sion

(di-men'shŭn)
Scope, size, magnitude; denoting, in the plural, linear measurements of length, width, and height.
References in periodicals archive ?
For processes valued in infinite-dimensional spaces, we can also give the example of hidden processes: let ([Z.sub.t]) be a nonobserved process valued in [R.sup.d], for which conditions of Theorem 5.3 in [21, page 136] hold for every x in a compact A, let T be an unknown function from [R.sup.d] to a space H (that can be infinite-dimensional) equipped with a semimetric d, and let ([X.sub.t]) = (r([Z.sub.t])) be an observed process.
On the other hand, many problems in mathematical physics and financial mathematics lead to the necessity of studying stochastic differential equations with operator coefficients in infinite-dimensional spaces. In [7], the authors generalize the classical Ito theory to this case.
They focus on recent developments in the theory of linear topological spaces, and the construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces. Their topics are the kernel theorem, nuclear spaces, and rigged Hilbert space; positive and positive-definite generalized functions; generalized random processes; and measures in linear topological spaces.