Intersection Local Times, Loop Soups and Permanental Wick Powers.
Jan, Yves Le.
Intersection Local Times, Loop Soups and Permanental Wick Powers. - 1st ed. - 1 online resource (92 pages) - Memoirs of the American Mathematical Society ; v.247 . - Memoirs of the American Mathematical Society .
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.
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 endowed with a metric d. Sufficient conditions are obtained for the continuity of these processes on (\mathcal,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.
9781470437039
Gaussian processes.
Electronic books.
QA274.4.L453 2017
519.23
Intersection Local Times, Loop Soups and Permanental Wick Powers. - 1st ed. - 1 online resource (92 pages) - Memoirs of the American Mathematical Society ; v.247 . - Memoirs of the American Mathematical Society .
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.
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 endowed with a metric d. Sufficient conditions are obtained for the continuity of these processes on (\mathcal,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.
9781470437039
Gaussian processes.
Electronic books.
QA274.4.L453 2017
519.23