Markov Processes and Potential Theory

By J. Doob, J. Chover. 2007

598 citations recorded by the source corpus.

Subfields: Management Information Systems, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a59d6653d9836924f97599e8fbe9c90fc1eaec8a

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In Management Information Systems

In Statistical and Nonlinear Physics

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Citations in the corpus

Brownian motions on metric graphs (2011, background): “By saying that X is a diffusion process we mean that X is a normal, strong Markov process (in the sense of [11]), a.”
Spectral properties of the Cauchy process on half‐line and interval (2009, methodology): “For the introduction to the notions of the Green operator and the Green function, the reader is referred to, for example, [6].”
Harmonic analysis of additive Lévy processes (2007, background): “by Blumenthal and Getoor [7], Doob [10], Fukushima, Ōshima, and Takeda [31], Getoor [32], and Röckner [88], together with their combined bibliography.”
Boundary Harnack principle for subordinate Brownian motions (2007, background): “3 in [2], which is polar in our case (Theorem 4.”
Potential Theory of Special Subordinators and Subordinate Killed Stable Processes (2006, background): “By the Riesz decomposition theorem (see, for instance, Chapter 6 of [6]), s = Gm + h, where m is a measure on D, and h is a nonnegative harmonic function for X.”
Neumann and Dirichlet Heat Kernels in Inner Uniform Domains (2011, background): “References for these considerations are [14, 13, 18, 19, 28, 81] among others.”
Random Fractals and Markov Processes (2005, unknown): “For the general theory of Markov processes, we refer to Blumenthal and Getoor (1968), Sharpe (1988) and Khoshnevisan (2002).”
On the relationship between subordinate killed and killed subordinate processes (2008, background): “Therefore, by an extended version of the strong Markov property (see [2], pp.”
Hitting probabilities for systems of non-linear stochastic heat equations with additive noise (2007, background): “See, for example Blumenthal and Getoor (1968), Port and Stone (1978), and Doob (1984). There is also a growing literature on the potential theory for multiparameter processes (Khoshnevisan (2002)). For the linear form of (1.1) (b ≡ 0, σ ≡ Id, where Id denotes the d × d identity matrix), results on h”
Estimates of the Green Function for the Fractional Laplacian Perturbed by Gradient (2010, background): “The joint distribution of (τD, XτD) defines the transition density of the process killed when leaving D ([27], [3], [22]): pD(t, x, y) = p(t, x, y)− E [τD < t; p(t− τD, XτD , y)], t > 0, x, y ∈ R d .”
Quasilimiting behavior for one-dimensional diffusions with killing (2010, unknown): “≤ lim T→∞ uλ 0 (a)Ex e−εTa∧T = uλκ 0 (a)Ex e−εTa (41) We now appeal to a basic fact from potential theory (stated and proved in much greater generality as Proposition D.15 of [16]; see also p. 285 of [6]): There is a constant C(a) such that for all x≥ a, (42) Ex e−εTa;T a <∞ = C(a)gε(x,a), where ”
Dynamic Markov bridges motivated by models of insider trading (2011, background): “Here we are using the formulation of a Markov process as given in, e.g., Blumenthal and Getoor [7] or Sharpe [21].”
A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options (2007, background): “MONTE CARLO ALGORITHMS FOR PRICING BERMUDAN OPTIONS 13 where Mt is the multiplicative functional Mt = 1{t<τA} for τA = inf{s ≥ 0|X0 s / ∈ [−A,A]d}; see, for instance, [1].”
Optimal stopping of Hunt and Lévy processes (2006, background): “In particular, X is a strong Markov process, quasi left continuous on [0,+∞) and the sample paths of X are right continuous with left limits (see Kunita and Watanabe [11] and Blumenthal and Getoor [2] p.”