scholarly journals Multiplicative free square of the free Poisson measure and examples of free symmetrization

2010 ◽  
Vol 119 (1) ◽  
pp. 127-136 ◽  
Author(s):  
Melanie Hinz ◽  
Wojciech Młotkowski
Keyword(s):  
Poisson Measure

DIFFEOMORPHISM GROUPS AND CURRENT ALGEBRAS: CONFIGURATION SPACE ANALYSIS IN QUANTUM THEORY

1999 ◽  
Vol 11 (01) ◽  
pp. 1-23 ◽  
Author(s):  
S. ALBEVERIO ◽  
YU. G. KONDRATIEV ◽  
M. RÖCKNER
Keyword(s):  
Differential Geometry ◽  
Quantum Theory ◽  
Configuration Space ◽  
Current Algebra ◽  
Relativistic Quantum ◽  
Unitary Representations ◽  
Poisson Measure ◽  
Diffeomorphism Groups ◽  
Dirichlet Operator ◽  
Space Analysis

The constuction of models of non-relativistic quantum fields via current algebra representations is presented using a natural differential geometry of the configuration space Γ of particles, the corresponding classical Dirichlet operator associated with a Poisson measure on Γ, being the free Hamiltonian. The case with interactions is also discussed together with its relation to the problem of unitary representations of the diffeomorphism group on ℝd.

scholarly journals On representation of integer-valued random measures by means of stochastic integrals with respect to the Poisson measure

1971 ◽  
Vol 11 (1) ◽  
pp. 93-108
Author(s):  
B. Grigelionis
Keyword(s):  
Stochastic Integrals ◽  
Poisson Measure ◽  
Random Measures

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Б. Григелионис. О представлении целочисленных случайных мер как стохастических интегралов по пуассоновской мере B. Grigelionis. Apie atsitiktinių matų su sveikomis reikšmėmis išreiškimų stochastiniais integralais Puasono mato atžvilgiu

Free powers of the free Poisson measure

2011 ◽  
Vol 123 (2) ◽  
pp. 285-290 ◽  
Author(s):  
Melanie Hinz ◽  
Wojciech Młotkowski
Keyword(s):  
Poisson Measure

Anticipated BDSDEs driven by Lévy process with non-Lipschitz coefficients

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Sadibou Aidara ◽  
Ahmadou Bamba Sow
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Lévy Process ◽  
Levy Process ◽  
Uniqueness Of Solution ◽  
Time Interval ◽  
Poisson Measure ◽  
Doubly Stochastic

AbstractIn this work we deal with a anticipated backward doubly stochastic differential equation associated to a random Poisson measure. We establish existence and uniqueness of solution in the case of non-Lipschitz coefficients. The novelty of our result lies in the fact that we allow the time interval to be infinite.

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