羊齿
发表于 2025-3-25 03:23:36
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
发表于 2025-3-25 09:05:20
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
发表于 2025-3-25 15:34:11
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
发表于 2025-3-25 18:27:46
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疼死我了
发表于 2025-3-25 21:44:48
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
发表于 2025-3-26 02:32:05
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
发表于 2025-3-26 05:05:24
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得体
发表于 2025-3-26 12:15:05
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
发表于 2025-3-26 14:09:00
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
发表于 2025-3-26 20:26:23
,Itô’s Lemma,As observed in Proposition . and Exercises ., . in Chapter ., the sample paths of Brownian motion are nowhere differentiable.