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This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are…
In this paper we consider quadratic stochastic operators designed on finite Abelian groups. It is proved that such operators have the property of regularity.
In this paper we introduce and discuss some classes of orthogonal polynomials in several non-commuting variables. The emphasis is on a non-commutative version of the orthogonal polynomials on the real line. We introduce recurrence equations…
Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional…
This thesis is mainly devoted to the study of the quantum properties of optical parametric oscillators (OPOs), which are nowadays the sources of the highest-quality quantum-correlated light, apart from fundamental tools in the…
A new approach to multi-dimensional quantum scattering by the infinite order discrete variable representation is presented. Determining the expansion coefficients of the wave function at the asymptotic regions by the solution of the…
In this work we study the persistence in time of superoscillations for the Schr\"{o}dinger equation with quadratic time-dependent Hamiltonians. We have solved explicitly the Cauchy initial value problem with three different kind of…
The paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the…
We discuss the necessity of using non-standard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
Using results from our companion article [arXiv:1112.4824v2] on a Schauder approach to existence of solutions to a degenerate-parabolic partial differential equation, we solve three intertwined problems, motivated by probability theory and…
Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally…
This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and…
The unique continuation on quadratic curves for harmonic functions is discussed in this paper. By using complex extension method, the conditional stability of unique continuation along quadratic curves for harmonic functions is illustrated.…
Existence and uniqueness theorems for quantum stochastic differential equations with nontrivial initial conditions are proved for coefficients with completely bounded columns. Applications are given for the case of finite-dimensional…
In this paper, we consider a class of stochastic midpoint and trapezoidal Lawson schemes for the numerical discretization of highly oscillatory stochastic differential equations. These Lawson schemes incorporate both the linear drift and…
In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…
We mostly survey results concerning the $L^2$ boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.
Monotone convex operators and time-consistent systems of operators appear naturally in stochastic optimization and mathematical finance in the context of pricing and risk measurement. We study the dual representation of a monotone convex…
This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…