Results 231 to 240 of about 70,159 (262)

OPERATOR PROCESSES MAJORIZING THEIR QUADRATIC VARIATION

Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2000
We give a full classification of convolution semigroups of completely positive mappings on Hopf algebras. Using the theory of noncommutative Lévy processes, we prove that these convolution semigroups are solutions of Hudson–Parthasarathy quantum stochastic differential equations. The generating process satisfies a positivity condition on the kernel of
openaire   +2 more sources

Variational Methods and Quadratic Functional Inequalities

SIAM Journal on Mathematical Analysis, 1975
In the context of a self-adjoint generalized differential system that is equivalent to a type of linear vector Riemann–Stieltjes integral equation, certain functional inequalities are presented generalizing, in particular, the well-known Liapunov inequality $\int_a^b q^ + (t)dt > {4 / {(b - a)}}$, which is satisfied by $q^ + (t) = \frac{1}{2}[q(t) + | {
openaire   +1 more source

Strong Martingales: Their Decompositions and Quadratic Variation

Journal of Theoretical Probability, 2001
The author considers a general framework of stochastic processes indexed by elements of a collection of closed subsets of a topological space. After defining a suitable form of predictability called \(^*\)-predictability, a kind of the Doob-Meyer decomposition \(X=M+V\) of a set-indexed strong submartingale \(X\) is obtained under an integrability ...
openaire   +1 more source

A Geometric Variational Problem with Logarithmic-Quadratic Interaction

SIAM Journal on Mathematical Analysis
The authors consider the functional \(\mathcal{J}(\Omega )=\mathcal{P}(\Omega )+\frac{\gamma }{2}\int_{\Omega }\int_{\Omega }K(\left\vert x-y\right\vert )dxdy\), defined on the admissible class \(\mathcal{A}=\{\Omega \subset \mathbb{R}^{2}:\Omega \) is Lebesgue measurable and \(\left\vert \Omega \right\vert =m\}\), \(m>0\).
Xiaofeng Ren, Chong Wang 0025, Juncheng Wei   +2 more
openaire   +1 more source

Quadratic Variation

SSRN Electronic Journal, 2020
Dilip B. Madan, King Wang
openaire   +1 more source

Singular quadratic variational problems

Journal of Optimization Theory and Applications, 1983
The purpose of this paper is to show that the general theory of quadratic forms developed earlier by the author is applicable to singular variational problems as well as to nonsingular ones. In particular, this general theory is applicable to the singular variational problems associated with Legendre polynomials, associated Legendre polynomials, Jacobi
openaire   +2 more sources

Total variation reconstruction from quadratic measurements

Numerical Algorithms, 2016
In this paper, we consider a problem of reconstructing an image from incomplete quadratic measurements by minimizing its total variation. The problem of reconstructing an object from incomplete nonlinear acquisitions arises in many applications, such as astronomical imaging or depth reconstruction.
openaire   +3 more sources

Stochastic Integrals and Quadratic Variation

2002
Continuous local martingales and semimartingales; quadratic variation and covariation; existence and basic properties of the integral; integration by parts and Ito’s formula; Fisk-Stratonovich integral; approximation and uniqueness; random time-change; dependence on ...
openaire   +1 more source

Quadratic variation along refining partitions: Constructions and examples

Journal of Mathematical Analysis and Applications, 2022
Purba Das, Rama Cont
exaly  

On the quadratic variation of semi-martingales

2010
Let X be a semi-martingale. Techniques of [1] and El Karoui (in [3] and [4]) are used to study the convergence of 2∊ times the number of upcrossings of [x, x+∊] by X to its local time at x. If X is continuous and if there exists a bicontinuous version of its local time process, then off a single null set, the convergence is shown to be uniform in x ...
openaire   +1 more source