Abstract: We study densely defined unbounded operators acting between different Hilbert spaces. For these, we introduce a notion of symmetric (closable) pairs of operators. The purpose of our paper is to give applications to selected themes at the cross road of operator commutation relations and stochastic calculus. We study a family of representations of the canonical commutation relations (CC...

‎This paper presents some results of an annihilated element in Banach algebra‎, ‎and in specific case‎, ‎for any square matrix‎. The developed method significantly improves the computational aspects of transformations calculus and especially for finding powers and roots of any annihilated element‎. ‎An example is given to compare the proposed method with some other methods to show the efficienc...

In this paper, we prove a central limit theorem for a sequence of multiple Skorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some applications to sequences of multiple stochastic integrals, and renormalized weighted quadratic variation of the fractional Brownian motion are discussed.

We study the concept of quadratic variation a continuous path along sequence partitions and its dependence with respect to choice partition sequence. introduce roughness show that for Hölder-continuous paths satisfying this condition, balanced is invariant Typical Brownian motion are shown satisfy property almost-surely any required step size condition. Using these results we derive formulation...

This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure Itô and Stratonovich integrals. In the second part, a survey and new results are presented in relation with finite quadratic variation processes, Dirichlet and weak Dirichlet processes.

Increasing sequences of contractive projections on a reflexive LP space share an unconditionality property similar to that exhibited sequences of self-adjoint projections on a Hilbert space. A slight variation of this property is shown to be precisely the correct condition on a reflexive Banach space to ensure that every operator with a contractive AC-functional calculus is scalar-type spectraL

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler–Lagrange equations are derived. Fractional equations are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives. PACS numbers: 45.20.−d, 45.20.Jj

It is shown that the index of a constrained critical point in the isoperimetric calculus of variations is simply related to the number of negative eigenvalues of a certain bordered operator associated with the second variation. A conjugate point theory for this bordered operator is then established.

We present a new modular proof method of termination for second-order computation, and report its implementation SOL. The is useful proving higher-order foundational calculi. To establish the method, we use variation semantic labelling translation Blanqui's General Schema: syntactic criterion strong normalisation. As an application, apply this to show variant call-by-push-value calculus with al...

We deal with stochastic differential equations jumps. In order to obtain an accurate approximation scheme, it is usual replace the “small jumps” by a Brownian motion. this paper, we prove that for every fixed time t, approximate random variable $$X^\varepsilon _t$$ converges original $$X_t$$ in total variation distance and estimate error. also give of between densities laws two variables. These...