General Mean Reflected BSDEs

The present paper is devoted to the study of backward stochastic differential equations with mean reflection formulated by Briand et al. [7]. We investigate the solvability of a generalized mean reflected BSDE, whose driver also depends on the distribution of the solution term $Y$. Using a fixed-point argument, BMO martingale theory and the $\theta$-method, we establish the existence and uniqueness result for such BSDEs in several typical situations, including the case where the driver is quadratic with bounded or unbounded terminal condition.Comment: 20 page

Active Defense Analysis of Blockchain Forking through the Spatial-Temporal Lens

Forking breaches the security and performance of blockchain as it is symptomatic of distributed consensus, spurring wide interest in analyzing and resolving it. The state-of-the-art works can be categorized into two kinds: experiment-based and model-based. However, the former falls short in exclusiveness since the derived observations are scenario-specific. Hence, it is problematic to abstractly reveal the crystal-clear forking laws. Besides, the models established in the latter are spatiality-free, which totally overlook the fact that forking is essentially an undesirable result under a given topology. Moreover, few of the ongoing studies have yielded to the active defense mechanisms but only recognized forking passively, which impedes forking prevention and cannot deter it at the source. In this paper, we fill the gap by carrying out the active defense analysis of blockchain forking from the spatial-temporal dimension. Our work is featured by the following two traits: 1) dual dimensions. We consider the spatiality of blockchain overlay network besides temporal characteristics, based on which, a spatial-temporal model for information propagation in blockchain is proposed; 2) active defense. We hint that shrinking the long-range link factor, which indicates the remote connection ability of a link, can cut down forking completely fundamentally. To the best of our knowledge, we are the first to inspect forking from the spatial-temporal perspective, so as to present countermeasures proactively. Solid theoretical derivations and extensive simulations are conducted to justify the validity and effectiveness of our analysis.Comment: 10 pages,10 figure