Page 1 Next

Displaying 1 – 20 of 24

Showing per page

Spatial trajectories

Rafael V. Chacon, Yves Le Jan, John B. Walsh (1981)

Séminaire de probabilités de Strasbourg

Stability estimating in optimal stopping problem

Elena Zaitseva (2008)

Kybernetika

We consider the optimal stopping problem for a discrete-time Markov process on a Borel state space X . It is supposed that an unknown transition probability p ( · | x ) , x X , is approximated by the transition probability p ˜ ( · | x ) , x X , and the stopping rule τ ˜ * , optimal for p ˜ , is applied to the process governed by p . We found an upper bound for the difference between the total expected cost, resulting when applying τ ˜ * , and the minimal total expected cost. The bound given is a constant times sup x X p ( · | x ) - p ˜ ( · | x ) , where · is the total variation...

Stability of solutions of BSDEs with random terminal time

Sandrine Toldo (2006)

ESAIM: Probability and Statistics

In this paper, we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely finite random terminal time. More precisely, we are going to show that if (Wn) is a sequence of scaled random walks or a sequence of martingales that converges to a Brownian motion W and if ( τ n ) is a sequence of stopping times that converges to a stopping time τ, then the solution of the BSDE driven by Wn with random terminal time τ n converges to the solution...

Strong tightness as a condition of weak and almost sure convergence

Grzegorz Krupa, Wiesław Zieba (1996)

Commentationes Mathematicae Universitatis Carolinae

A sequence of random elements { X j , j J } is called strongly tight if for an arbitrary ϵ > 0 there exists a compact set K such that P j J [ X j K ] > 1 - ϵ . For the Polish space valued sequences of random elements we show that almost sure convergence of { X n } as well as weak convergence of randomly indexed sequence { X τ } assure strong tightness of { X n , n } . For L 1 bounded Banach space valued asymptotic martingales strong tightness also turns out to the sufficient condition of convergence. A sequence of r.e. { X n , n } is said to converge essentially with...

Currently displaying 1 – 20 of 24

Page 1 Next