Titlebook: Continuous Parameter Markov Processes and Stochastic Differential Equations; Rabi Bhattacharya,Edward C. Waymire Textbook 2023 Springer Na

羊齿

https://doi.org/10.1007/978-3-322-86393-5In this chapter, based mostly on Wasielak (.) and Bhattacharya and Wasielak (.), criteria for polynomial and exponential rates of convergence of Markov processes to equilibrium are derived both for discrete time Harris positive recurrent Markov processes, as well as .-dimensional diffusions, ., using the method of coupling.

兽皮

https://doi.org/10.1007/978-3-322-86394-2The classical Dirichlet problem seeks to find functions with specified boundary values on a domain for which the function is harmonic on the interior. The intrinsic connection between the Laplacian operator and Brownian motion leads to a beautiful interplay between pde and stochastic calculus presented in this chapter.

DAUNT

https://doi.org/10.1007/978-3-322-86395-9In this chapter the theory of stochastic integrals is extended to that with respect to square integrable martingales. This extension is enabled by the so called Doob–Meyer decomposition of submartingales

吗啡

疼死我了

Semigroup Theory and Markov Processes,To construct a discrete parameter homogeneous Markov process with state space (., one only needs to specify the initial state, or initial distribution, and the one-step transition probability . (see BCPT, pp. 187–189, or Bhattacharya and Waymire ., pp. 9–11).

Ptosis

Regularity of Markov Process Sample Paths,In this chapter, Markov processes, having a locally compact, separable state space, are constructed with right-continuous sample paths having left limits, often referred to as..

Accord

得体

Processes with Independent Increments,Let us begin by revisiting some essential examples of processes with independent increments from the perspective of the present chapter.

Pseudoephedrine

The Stochastic Integral,In this chapter, Itô’s stochastic integral and some of its basic properties are carefully introduced. The essential role of martingale theory is made manifestly clear through this development.

思想流动

,Itô’s Lemma,As observed in Proposition . and Exercises ., . in Chapter ., the sample paths of Brownian motion are nowhere differentiable.