A framework of BSDEs with stochastic Lipschitz coefficients
ESAIM: Probability and Statistics, Tome 24 (2020), pp. 739-769.

In this paper, we suggest an effective technique based on random time-change for dealing with a large class of backward stochastic differential equations (BSDEs for short) with stochastic Lipschitz coefficients. By means of random time-change, we show the relation between the BSDEs with stochastic Lipschitz coefficients and the ones with bounded Lipschitz coefficients and stopping terminal time, so they are possible to be exchanged with each other from one type to another. In other words, the stochastic Lipschitz condition is not essential in the context of BSDEs with random terminal time. Using this technique, we obtain a couple of new results of BSDEs with stochastic Lipschitz (or monotone) coefficients.

DOI : 10.1051/ps/2020016
Classification : 60H05, 60H20
Mots-clés : Backward stochastic differential equations (BSDEs), time-change, stochastic Lipschitz coefficient, random terminal time, Markov chain 
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     title = {A framework of {BSDEs} with stochastic {Lipschitz} coefficients},
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O, Hun; Kim, Mun-Chol; Pak, Chol-Kyu. A framework of BSDEs with stochastic Lipschitz coefficients. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 739-769. doi : 10.1051/ps/2020016. http://archive.numdam.org/articles/10.1051/ps/2020016/

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