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Markov Processes, Feller Semigroups and Evolution Equations cover

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.


Contents:
  • Introduction:
    • Introduction: Stochastic Differential Equations
  • Strong Markov Processes:
    • Strong Markov Processes on Polish Spaces
    • Strong Markov Processes: Proof of Main Results
    • Space-Time Operators and Miscellaneous Topics
  • Backward Stochastic Differential Equations:
    • Feynman–Kac Formulas, Backward Stochastic Differential Equations and Markov Processes
    • Viscosity Solutions, Backward Stochastic Differential Equations and Markov Processes
    • The Hamilton–Jacobi–Bellman Equation and the Stochastic Noether Theorem
  • Long Time Behavior:
    • On Non-Stationary Markov Processes and Dunford Projections
    • Coupling Methods and Sobolev Type Inequalities
    • Invariant Measure

Readership: Graduate students and researchers in mathematical physics, mathematics and statistics.

Free Access
FRONT MATTER
  • Pages:i–xviii

https://doi.org/10.1142/9789814322195_fmatter

Introduction


No Access
Introduction: Stochastic differential equations
  • Pages:3–106

https://doi.org/10.1142/9789814322195_0001

Strong Markov Processes


No Access
Strong Markov processes on Polish spaces
  • Pages:109–165

https://doi.org/10.1142/9789814322195_0002

No Access
Strong Markov processes: Proof of main results
  • Pages:167–225

https://doi.org/10.1142/9789814322195_0003

No Access
Space-time operators and miscellaneous topics
  • Pages:227–300

https://doi.org/10.1142/9789814322195_0004

Backward Stochastic Differential Equations


No Access
Feynman-Kac formulas, backward stochastic differential equations and Markov processes
  • Pages:303–383

https://doi.org/10.1142/9789814322195_0005

No Access
Viscosity solutions, backward stochastic differential equations and Markov processes
  • Pages:385–406

https://doi.org/10.1142/9789814322195_0006

No Access
The Hamilton-Jacobi-Bellman equation and the stochastic Noether theorem
  • Pages:407–450

https://doi.org/10.1142/9789814322195_0007

Long Time Behavior


No Access
On non-stationary Markov processes and Dunford projections
  • Pages:453–554

https://doi.org/10.1142/9789814322195_0008

No Access
Coupling methods and Sobolev type inequalities
  • Pages:555–645

https://doi.org/10.1142/9789814322195_0009

No Access
Invariant measure
  • Pages:647–758

https://doi.org/10.1142/9789814322195_0010

Free Access
BACK MATTER
  • Pages:759–805

https://doi.org/10.1142/9789814322195_bmatter

“This book is a valuable contribution to the theory of (time-inhomogeneous) Markov processes. It presents a wide range of concepts and ideas that are connected to parabolic diffusion equations and their probabilistic counterparts. The book certainly provides a solid starting basis for further, more conceptual research on time-inhomogeneous Markov processes due to many interesting remarks and instructive hints provided by the author.”
MathSciNet