TY  - BOOK
AU  - Jan,Yves Le
AU  - Marcus,Michael B.
AU  - Rosen,Jay
TI  - Intersection Local Times, Loop Soups and Permanental Wick Powers
T2  - Memoirs of the American Mathematical Society
SN  - 9781470437039
AV  - QA274.4.L453 2017 
U1  - 519.23 
PY  - 2017///
CY  - Providence
PB  - American Mathematical Society
KW  - Gaussian processes
KW  - Electronic books
N1  - Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Loop measures and renormalized intersection local times -- 2.1. Renormalized intersection local times -- 2.2. Bounds for the error terms -- Chapter 3. Continuity of intersection local time processes -- Chapter 4. Loop soup and permanental chaos -- Chapter 5. Isomorphism Theorem I -- Chapter 6. Permanental Wick powers -- Chapter 7. Poisson chaos decomposition, I -- Chapter 8. Loop soup decomposition of permanental Wick powers -- Chapter 9. Poisson chaos decomposition, II -- 9.1. Exponential Poisson chaos -- 9.2. Extensions to martingales -- Chapter 10. Convolutions of regularly varying functions -- References -- Back Cover
N2  - Several stochastic processes related to transient Lévy processes with potential densities u(x,y)=u(y-x), that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures \mathcal{V} endowed with a metric d. Sufficient conditions are obtained for the continuity of these processes on (\mathcal{V},d). The processes include n-fold self-intersection local times of transient Lévy processes and permanental chaoses, which are `loop soup n-fold self-intersection local times' constructed from the loop soup of the Lévy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of n-th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908293
ER  -