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Handbook of Brownian Motion - Facts and Formulae
I: Theory.- I. Stochastic processes in general.- II. Linear diffusions.- III. Stochastic calculus.- IV. Brownian motion.- V. Local time as a Markov process.- VI. Differential systems associated toExpand
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Handbook of Brownian Motion - Facts and Formulae (Second Edition)
Brownian motion as well as other diffusion processes play a meaningful role in stochastic analysis. They are very important from theoretical point of view and very useful in applications. DiffusionsExpand
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Optimal Stopping of One‐Dimensional Diffusions
In this paper we consider an optimal stopping problem for a time-homogeneous, onedimensional, regular diffusion. An essential tool in our approach is the MARTIN boundary theory. It is possible toExpand
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Properties of perpetual integral functionals of Brownian motion with drift
Abstract In this paper we study integrability properties of the random variable I ∞ ( f ) : = ∫ 0 ∞ f ( B t ( μ ) ) d t , where { B t ( μ ) : t ⩾ 0 } is a Brownian motion with drift μ > 0 and f is aExpand
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Optimal stopping of strong Markov processes
We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The mainExpand
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On the excursion theory for linear diffusions
Abstract.We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail.Expand
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Optimal stopping of Hunt and Lévy processes
Infinite horizon (perpetual) optimal stopping problems for Hunt processes on R are studied via the representation theory of excessive functions. In particular, we focus on problems with one-sidedExpand
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On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary t ↦ a + bt, a ≥ 0, b ∈ ℝ, by a reflecting Brownian motion. The main tool hereby is Doob’sExpand
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On fractional Ornstein-Uhlenbeck processes
In this paper we study Doob's transform of fractional Brownian motion (FBM). It is well known that Doob's transform of standard Brownian motion is identical in law with the Ornstein-UhlenbeckExpand
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On maximum increase and decrease of Brownian motion
The joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at the hitting timesExpand
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