Alexander G. Sokol

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We give a causal interpretation of stochastic differential equations (SDEs) by defining the postintervention SDE resulting from an intervention in an SDE. We show that under Lipschitz conditions, the solution to the postintervention SDE is equal to a uniform limit in probability of postintervention structural equation models based on the Euler scheme of the(More)
PURPOSE We assessed the impact of prostate size on operative difficulty as measured by estimated blood loss, operating room time and positive surgical margins. In addition, we assessed the impact on biochemical recurrence and the functional outcomes of potency and continence at 1 year after radical prostatectomy as well as postoperative bladder neck(More)
Subduction tectonics imposes an important role in the evolution of the interior of the Earth and its global carbon cycle; however, the mechanism of the mantle-slab interaction remains unclear. Here, we demonstrate the results of high-pressure redox-gradient experiments on the interactions between Mg-Ca-carbonate and metallic iron, modeling the processes at(More)
Analysis of data on micro- and nano-inclusions in mantle-derived and metamorphic diamonds shows that, to a first approximation, diamond-forming medium can be considered as a specific ultrapotassic, carbonate/chloride/silicate/water fluid. In the present work, the processes and mechanisms of diamond crystallization were experimentally studied at 7.5 GPa,(More)
We give sufficient criteria for the Doléans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are sufficiently weak to be useful and verifiable, as illustrated by several non-trivial examples, without introducing artificial constraints. In particular, they make it possible to(More)
Deep carbon and nitrogen cycles played a critical role in the evolution of the Earth. Here we report on successful studying of speciation in C-O-H-N systems with low nitrogen contents at 6.3 GPa and 1100 to 1400 °C. At fO2 near Fe-FeO (IW) equilibrium, the synthesised fluids contain more than thirty species. Among them, CH4, C2H6, C3H8 and C4H10 are main(More)
results in ergodic theory as presented in Chapter 2 can be found in Breiman (1968) and Loève (1977b). A major application of ergodic theory is to the theory of the class of stochastic processes known as Markov processes. In Markov process theory, stationary processes are frequently encountered, and thus the theory presents an opportunity for utilizing the(More)