A beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. For such operators regular and singular perturbations of order zero and their spectral properties are investigated. A complete treatment of the Feynman-Kac formula is given. The theory is applied to such topics as compactness or trace class properties...
A beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the othe...
The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. This mathematical material finds its applications in several branches of the scientific world among which mathematical physics, hedging models in financial mathematics, population models.
The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the li...
