2017; 78 pp; Softcover
MSC: Primary 60;
Print ISBN: 978-1-4704-3695-7
Product Code: MEMO/247/1171
List Price: $75.00
AMS Member Price: $45.00
MAA Member Price: $67.50
Electronic ISBN: 978-1-4704-3703-9
Product Code: MEMO/247/1171.E
List Price: $75.00
AMS Member Price: $45.00
MAA Member Price: $67.50
Intersection Local Times, Loop Soups and Permanental Wick Powers
Share this pageYves Le Jan; Michael B. Marcus; Jay Rosen
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.
Table of Contents
Table of Contents
Intersection Local Times, Loop Soups and Permanental Wick Powers
- Cover Cover11
- Title page i2
- Chapter 1. Introduction 18
- Chapter 2. Loop measures and renormalized intersection local times 714
- Chapter 3. Continuity of intersection local time processes 2532
- Chapter 4. Loop soup and permanental chaos 2936
- Chapter 5. Isomorphism Theorem I 3340
- Chapter 6. Permanental Wick powers 3542
- Chapter 7. Poisson chaos decomposition, I 4552
- Chapter 8. Loop soup decomposition of permanental Wick powers 5360
- Chapter 9. Poisson chaos decomposition, II 6168
- Chapter 10. Convolutions of regularly varying functions 6774
- References 7784
- Back Cover Back Cover192