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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 $p (\cdot | x)$ , $x \in X$ , is approximated by the transition probability $\tilde{p} (\cdot | x)$ , $x \in X$ , and the stopping rule ${\tilde{τ}}_{*}$ , optimal for $\tilde{p}$ , is applied to the process governed by $p$ . We found an upper bound for the difference between the total expected cost, resulting when applying ${\tilde{τ}}_{*}$ , and the minimal total expected cost. The bound given is a constant times ${sup}_{x \in X} ∥ p (\cdot | x) - \tilde{p} (\cdot | x) ∥$ , where $∥ \cdot ∥$ 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...

State tameness: a new approach for credit constrains.

Londoño, Jaime A. (2004)

Electronic Communications in Probability [electronic only]

Stationary Markov sets

Michael I. Taksar (1987)

Séminaire de probabilités de Strasbourg

Stopping problems as special statistical decision problems

Peter Neumann (1985)

Banach Center Publications

Stopping sequences

Hermann Dinges (1974)

Séminaire de probabilités de Strasbourg

Stopping times with given laws

Richard M. Dudley, Sam Gutmann (1977)

Séminaire de probabilités de Strasbourg

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 ${X_{j}, j \in J}$ is called strongly tight if for an arbitrary $ϵ > 0$ there exists a compact set $K$ such that $P (⋂_{j \in J} [X_{j} \in K]) > 1 - ϵ$ . 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 ${X_{n}, n \in ℕ}$ . 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. ${X_{n}, n \in ℕ}$ is said to converge essentially with...

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Semi-group methods in stochastic control

Skorohod embedding in Brownian motion in $R^{n}$

Skorokhod stopping in discrete time

Skorokhod stopping times of minimal variance

Skorokhod stopping via potential theory

Some new Chacon-Edgar-type inequalities for stochastic processes, and characterizations of Vitali-conditions

Some universal field equations

Spatial trajectories

Stability and other limit laws for exit times of random walks from a strip or a halfplane

Stability estimating in optimal stopping problem

Stability of solutions of BSDEs with random terminal time

State tameness: a new approach for credit constrains.

Stationary Markov sets

Stopping problems as special statistical decision problems

Stopping sequences

Stopping times with given laws

Strong tightness as a condition of weak and almost sure convergence

Sur des problèmes de régularisation, de recollement et d'interpolation en théorie des processus

Sur la démonstration de prévisibilité de Chung et Walsh

Sur l'approximation des réduites

Currently displaying 1 – 20 of 24