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Handbook of Brownian Motion - Facts and Formulae

- A. Borodin, P. Salminen
- Mathematics
- 1 June 1996

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 to… Expand

Handbook of Brownian Motion - Facts and Formulae (Second Edition)

- A. Borodin, P. Salminen
- Mathematics
- 2003

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. Diffusions… Expand

- 127
- 26
- PDF

Optimal Stopping of One‐Dimensional Diffusions

- P. Salminen
- Mathematics
- 1985

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 to… Expand

Properties of perpetual integral functionals of Brownian motion with drift

- P. Salminen, M. Yor
- Mathematics
- 1 May 2005

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 a… Expand

Optimal stopping of strong Markov processes

- S. Christensen, P. Salminen, B. Ta
- Mathematics
- 21 March 2012

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 main… Expand

On the excursion theory for linear diffusions

- P. Salminen, P. Vallois, M. Yor
- Mathematics
- 22 December 2006

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

Optimal stopping of Hunt and Lévy processes

- E. Mordecki, P. Salminen
- Mathematics
- 2 May 2006

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-sided… Expand

On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes

- P. Salminen, M. Yor
- Computer Science, Mathematics
- Period. Math. Hung.
- 9 December 2010

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’s… Expand

On fractional Ornstein-Uhlenbeck processes

- Terhi Kaarakka, P. Salminen
- Mathematics, Physics
- 26 October 2007

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-Uhlenbeck… Expand

On maximum increase and decrease of Brownian motion

- P. Salminen, P. Vallois
- Mathematics
- 19 December 2005

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 times… Expand