A Generalized White Noise Space Approach To Stochastic Integration For A Class Of Gaussian Stationary Increment Processes,
2013
Chapman University
A Generalized White Noise Space Approach To Stochastic Integration For A Class Of Gaussian Stationary Increment Processes, Daniel Alpay, Alon Kipnis
Mathematics, Physics, and Computer Science Faculty Articles and Research
Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô calculus rules, can be naturally defined using ideas taken from Hida’s white noise space theory. We use the Bochner-Minlos theorem to associate a probability space to the process, and define the counterpart of the S-transform in this space. We then use this transform to define the stochastic integral and prove an associated Itô formula.
Convex Cones Of Generalized Positive Rational Functions And Nevanlinna-Pick Interpolation,
2013
Chapman University
Convex Cones Of Generalized Positive Rational Functions And Nevanlinna-Pick Interpolation, Daniel Alpay, Izchak Lewkowicz
Mathematics, Physics, and Computer Science Faculty Articles and Research
Scalar rational functions with a non-negative real part on the right half plane, called positive, are classical in the study of electrical networks, dissipative systems, Nevanlinna-Pick interpolation and other areas. We here study generalized positive functions, i.e with a non-negative real part on the imaginary axis. These functions form a Convex Invertible Cone, cic in short, and we explore two partitionings of this set: (i) into (infinitely many non-invertible) convex cones of functions with prescribed poles and zeroes in the right half plane and (ii) each generalized positive function can be written as a sum of even and odd parts. …
Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory,
2013
Chapman University
Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.
Representation Formulas For Hardy Space Functions Through The Cuntz Relations And New Interpolation Problems,
2013
Chapman University
Representation Formulas For Hardy Space Functions Through The Cuntz Relations And New Interpolation Problems, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Itzik Marziano
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce connections between the Cuntz relations and the Hardy space H2 of the open unit disk D. We then use them to solve a new kind of multipoint interpolation problem in H2, where for instance, only a linear combination of the values of a function at given points is preassigned, rather than the values at the points themselves.
A Representation For Positive Functionals Of A Brownian Motion And An Application,
2012
Louisiana State University
A Representation For Positive Functionals Of A Brownian Motion And An Application, P Sundar, Ming Tao
Communications on Stochastic Analysis
No abstract provided.
Lattice Modules Over Rings Of Bounded Random Variables,
2012
Louisiana State University
Lattice Modules Over Rings Of Bounded Random Variables, Karl-Theodor Eisele, Sonia Taieb
Communications on Stochastic Analysis
No abstract provided.
Spectral Multipliers For The Dunkl Laplacian,
2012
Louisiana State University
Spectral Multipliers For The Dunkl Laplacian, Sallam Hassani, Mohamed Sifi
Communications on Stochastic Analysis
No abstract provided.
Bose-Einstein Condensation: A Transition To Chaos Result,
2012
Louisiana State University
Bose-Einstein Condensation: A Transition To Chaos Result, Stefania Ugolini
Communications on Stochastic Analysis
No abstract provided.
The Feynman Integrand For The Charged Particle In A Constant Magnetic Field As White Noise Distribution,
2012
Louisiana State University
The Feynman Integrand For The Charged Particle In A Constant Magnetic Field As White Noise Distribution, Wolfgang Bock, Martin Grothaus, Sebastian Jung
Communications on Stochastic Analysis
No abstract provided.
Cauchy Problem And Integral Representation Associated To The Power Of The Qwn-Euler Operator,
2012
Louisiana State University
Cauchy Problem And Integral Representation Associated To The Power Of The Qwn-Euler Operator, Aymen Ettaieb, Habib Ouerdiane, Hafedh Rguigui
Communications on Stochastic Analysis
No abstract provided.
Generalized Field Operator Associated To The Fractional Lévy Processes,
2012
Louisiana State University
Generalized Field Operator Associated To The Fractional Lévy Processes, Mounir Dahwathi, Souheyl Jendoubi, Habib Ouerdiane, Anis Riahi
Communications on Stochastic Analysis
No abstract provided.
Numerical Methods For Optimal Insurance Demand Under Marked Point Processes Shocks,
2012
Louisiana State University
Numerical Methods For Optimal Insurance Demand Under Marked Point Processes Shocks, Mohamed Mnif
Communications on Stochastic Analysis
No abstract provided.
Preface,
2012
Louisiana State University
Clark-Ocone Formula By The S-Transform On The Poisson White Noise Space,
2012
Louisiana State University
Clark-Ocone Formula By The S-Transform On The Poisson White Noise Space, Yuh-Jia Lee, Nicolas Privault, Hsin-Hung Shih
Communications on Stochastic Analysis
No abstract provided.
Lieb-Thirring Bound For Schrödinger Operators With Bernstein Functions Of The Laplacian,
2012
Louisiana State University
Lieb-Thirring Bound For Schrödinger Operators With Bernstein Functions Of The Laplacian, Fumio Hiroshima, József Lorinczi
Communications on Stochastic Analysis
No abstract provided.
Backward Stochastic Differential Equations With Respect To General Filtrations And Applications To Insider Finance,
2012
Louisiana State University
Backward Stochastic Differential Equations With Respect To General Filtrations And Applications To Insider Finance, Bernt Øksendal, Tusheng Zhang
Communications on Stochastic Analysis
No abstract provided.
The Itô Formula For A New Stochastic Integral,
2012
Louisiana State University
The Itô Formula For A New Stochastic Integral, Hui-Hsiung Kuo, Anuwat Sae-Tang, Benedykt Szozda
Communications on Stochastic Analysis
No abstract provided.
On The Numerical Solution Of Linear Fredholm-Volterra İntegro Differential Difference Equations With Piecewise İntervals,
2012
Mugla University
On The Numerical Solution Of Linear Fredholm-Volterra İntegro Differential Difference Equations With Piecewise İntervals, Mustafa Gülsu, Yalçın Öztürk
Applications and Applied Mathematics: An International Journal (AAM)
The numerical solution of a mixed linear integro delay differential-difference equation with piecewise interval is presented using the Chebyshev collocation method. The aim of this article is to present an efficient numerical procedure for solving a mixed linear integro delay differential difference equations. Our method depends mainly on a Chebyshev expansion approach. This method transforms a mixed linear integro delay differential-difference equations and the given conditions into a matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system …
Sample Path Properties Of Volterra Processes,
2012
Louisiana State University
Sample Path Properties Of Volterra Processes, Leonid Mytnik, Eyal Neuman
Communications on Stochastic Analysis
No abstract provided.
Feynman-Kac Formula For The Solution Of Cauchy's Problem With Time Dependent Lévy Generator,
2012
Louisiana State University
Feynman-Kac Formula For The Solution Of Cauchy's Problem With Time Dependent Lévy Generator, Aroldo Pérez
Communications on Stochastic Analysis
No abstract provided.
