Coquet, François; Toldo, Sandrine Convergence of values in optimal stopping and convergence of optimal stopping times. (English) Zbl 1144.62067 Electron. J. Probab. 12, 207-228 (2007). In this paper the problem of stability of values of optimal stopping, and of optimal stopping times, under approximations of the process \(X\) are investigated [see D. Lamberton and G. Pagès, Sur l’approximation des réduites. Ann. Inst. Henri Poincaré, Probab. Stat. 26, No. 2, 331–355 (1990; Zbl 0704.60042)]. Let us consider a sequence \((X^n)_n\) of càdlàg processes which converges in probability to a càdlàg process \(X\). For all \(n\), let us denote by \({\mathcal F}^n\) the natural filtration of \(X^n\) and by \({\mathcal T}^n_T\) the set of \({\mathcal F}^n\) stopping times bounded by \(T\). Denote the values in the optimal stopping problem \(\Gamma^n(T)= \sup_{\tau\in {\mathcal T}^n_T}{\mathbf E}[\gamma(\tau,X_\tau^n)]\).In this paper first are given conditions under which \(\Gamma^n(T)\) converges to \(\Gamma(T)\), and second, when it is possible to find a sequence \((\tau_n)\) of optimal stopping times w.r.t. the \(X^n\), to give further conditions under which the sequence \((\tau_n)\) converges to an optimal stopping time w.r.t \(X\). The results are obtained under hypothesis of inclusion of filtrations or convergence of filtrations. Reviewer: Krzysztof Szajowski (Wrocław) Cited in 1 ReviewCited in 14 Documents MSC: 62L15 Optimal stopping in statistics 60G40 Stopping times; optimal stopping problems; gambling theory 60Fxx Limit theorems in probability theory 91A60 Probabilistic games; gambling 91A80 Applications of game theory Keywords:values of optimal stopping; convergence of stochastic processes; convergence of filtrations; optimal stopping times; convergence of stopping times; Skorokhod topology Citations:Zbl 0704.60042 × Cite Format Result Cite Review PDF Full Text: DOI arXiv EuDML