Passive discrete-time systems with a Pontryagin state space

Passive discrete-time systems with Hilbert spaces as an incoming and outgoing space and a Pontryagin space as a state space are investigated. A geometric characterization when the index of the transfer function coincides with the negative index of the state space is given. In this case, an isometric (co-isometric) system has a product representation corresponding to the left (right) Krein-Langer factorization of the transfer function. A new criterion, based on the inclusion of reproducing kernel spaces, when a product of two isometric (co-isometric) systems preserves controllability (observability), is obtained. The concept of the defect function is expanded for generalized Schur functions, and realizations of generalized Schur functions with zero defect functions are studied

Necessary and Sufficient Conditions for H\"older Continuity of Gaussian Processes

The continuity of Gaussian processes is extensively studied topic and it culminates in the Talagrand's notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the H\"older continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov-\v{C}entsov condition

Representation of self-similar Gaussian processes

We develop the canonical Volterra representation for a self-similar Gaussian process by using the Lamperti transformation of the corresponding stationary Gaussian process, where this latter one admits a canonical integral representation under the assumption of pure non-determinism. We apply the representation obtained for the self-similar Gaussian process to derive an expression for Gaussian processes that are equivalent in law to the self-similar Gaussian process in question

Stein's method on the second Wiener chaos : 2-Wasserstein distance

In the first part of the paper we use a new Fourier technique to obtain a Stein characterizations for random variables in the second Wiener chaos. We provide the connection between this result and similar conclusions that can be derived using Malliavin calculus. We also introduce a new form of discrepancy which we use, in the second part of the paper, to provide bounds on the 2-Wasserstein distance between linear combinations of independent centered random variables. Our method of proof is entirely original. In particular it does not rely on estimation of bounds on solutions of the so-called Stein equations at the heart of Stein's method. We provide several applications, and discuss comparison with recent similar results on the same topic

Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions

We show that every multiparameter Gaussian process with integrable variance function admits a Wiener integral representation of Fredholm type with respect to the Brownian sheet. The Fredholm kernel in the representation can be constructed as the unique symmetric square root of the covariance. We analyze the equivalence of multiparameter Gaussian processes by using the Fredholm representation and show how to construct series expansions for multiparameter Gaussian processes by using the Fredholm kernel.Comment: Published at http://dx.doi.org/10.15559/15-VMSTA39CNF in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/

Hedging in fractional Black-Scholes model with transaction costs

We consider conditional-mean hedging in a fractional Black-Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the recently discovered explicit conditional law of the fractional Brownian motion

Conditional-Mean Hedging Under Transaction Costs in Gaussian Models

We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an application, we consider conditional-mean hedging under transaction costs in Black-Scholes type pricing models where the Brownian motion is replaced with a more general regular invertible Gaussian Volterra process.Comment: arXiv admin note: text overlap with arXiv:1706.0153

Generalization of the Nualart-Peccati criterion

The celebrated Nualart-Peccati criterion [Ann. Probab. 33 (2005) 177-193] ensures the convergence in distribution toward a standard Gaussian random variable $N$ of a given sequence $\{X_n\}_{n\ge1}$ of multiple Wiener-It\^{o} integrals of fixed order, if $\mathbb {E}[X_n^2]\to1$ and $\mathbb {E}[X_n^4]\to \mathbb {E}[N^4]=3$. Since its appearance in 2005, the natural question of ascertaining which other moments can replace the fourth moment in the above criterion has remained entirely open. Based on the technique recently introduced in [J. Funct. Anal. 266 (2014) 2341-2359], we settle this problem and establish that the convergence of any even moment, greater than four, to the corresponding moment of the standard Gaussian distribution, guarantees the central convergence. As a by-product, we provide many new moment inequalities for multiple Wiener-It\^{o} integrals. For instance, if $X$ is a normalized multiple Wiener-It\^{o} integral of order greater than one, $$\forall k\ge2,\qquad \mathbb {E}\bigl[X^{2k}\bigr]>\mathbb {E} \bigl[N^{2k}\bigr]=(2k-1)!!.$$Comment: Published at http://dx.doi.org/10.1214/14-AOP992 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Make-or-buy configurational approaches in product-service ecosystems and performance

This research examines firm boundary configurations for manufacturers' product-service offerings. We argue that the building of a product-service ecosystem through collaboration with service providers in certain types of business services can increase performance as a result of the superior knowledge-based resources coming from specialized partners. By using fuzzy set qualitative analysis on a sample of 370 multinational manufacturing enterprises (MMNEs), the results reveal that effective servitization is heterogeneous across manufacturing industries and across business service offerings. The findings indicate that most industries achieve their highest performance through collaborations with value-added service providers in two out of three of the service continuum stages (Base and Intermediate services); while keeping the development of Advanced services in-house. The results help to contextualize the best practices for implementing service business models in MMNEs by detailing which service capabilities should be retained in-house and which should be outsourced to specialized partners in various industrial contexts.Peer ReviewedPreprin

Sensor Networks TDOA Self-Calibration: 2D Complexity Analysis and Solutions

Given a network of receivers and transmitters, the process of determining their positions from measured pseudo-ranges is known as network self-calibration. In this paper we consider 2D networks with synchronized receivers but unsynchronized transmitters and the corresponding calibration techniques,known as TDOA techniques. Despite previous work, TDOA self-calibration is computationally challenging. Iterative algorithms are very sensitive to the initialization, causing convergence issues.In this paper, we present a novel approach, which gives an algebraic solution to three previously unsolved scenarios. Our solvers can lead to a position error <1.2% and are robust to noise