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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.
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. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.
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.
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