Continuous state branching processes in random environment: The Brownian case

We consider continuous state branching processes that are perturbed by a Brownian motion. These processes are constructed as the unique strong solution of a stochastic differential equation. The long-term extinction and explosion behaviours are studied. In the stable case, the extinction and explosion probabilities are given explicitly. We find three regimes for the asymptotic behaviour of the explosion probability and, as in the case of branching processes in random environment, we find five regimes for the asymptotic behaviour of the extinction probability. In the supercritical regime, we study the process conditioned on eventual extinction where three regimes for the asymptotic behaviour of the extinction probability appear. Finally, the process conditioned on non-extinction and the process with immigration are given.Comment: New version, Theorem 1 is improved and a new regime appears in the supercritical cas

Asymptotic behaviour of exponential functionals of L\'evy processes with applications to random processes in random environment

Let $\xi=(\xi_t, t\ge 0)$ be a real-valued L\'evy process and define its associated exponential functional as follows $$I_t(\xi):=\int_0^t \exp\{-\xi_s\}{\rm d} s, \qquad t\ge 0.$$ Motivated by important applications to stochastic processes in random environment, we study the asymptotic behaviour of $$\mathbb{E}\Big[F\big(I_t(\xi)\big)\Big] \qquad \textrm{as}\qquad t\to \infty,$$ where $F$ is a non-increasing function with polynomial decay at infinity and under some exponential moment conditions on $\xi$. In particular, we find five different regimes that depend on the shape of the Laplace exponent of $\xi$. Our proof relies on a discretisation of the exponential functional $I_t(\xi)$ and is closely related to the behaviour of functionals of semi-direct products of random variables. We apply our main result to three {questions} associated to stochastic processes in random environment. We first consider the asymptotic behaviour of extinction and explosion for {stable} continuous state branching processes in a L\'evy random environment. Secondly, we {focus on} the asymptotic behaviour of the mean of a population model with competition in a L\'evy random environment and finally, we study the tail behaviour of the maximum of a diffusion process in a L\'evy random environment.Comment: arXiv admin note: text overlap with arXiv:1512.07691, arXiv:math/0511265 by other authors. Results are improve

Transactional, Social, and Legal Aspects of Oil Exploration and Extraction in Colombia

In Colombia, as in many other countries with oil reserves potential, the government has sought to reduce the activity\u27s inherent high degree of un-certainty by shaping the legal and economic environment that foreign com-panies have to operate in, making it more profitable and attractive for them.16 This paper seeks to accurately represent this environment to the pro-spective investor, starting with the structures of the two basic transactions, referred to herein as modes , through which most commonly, foreign com-panies participate in the oil industry in Colombia, namely, the Standard As-sociation Mode ( S.A.M ) and the Risk Sharing Mode ( R.S.M. ).17 The contractual agreements corresponding to these modes are standardized and allow little tailoring to fit individual company needs. This part of the analysis will also include recent modifications to the foregoing modes, introduced to meet the government\u27s announced oil-policy objectives of increasing production, exploiting the existing reserves, and finding additional ones. In addition, a brief examination of the taxation re-gime will be followed by a discussion of the regulation implemented to pro- tect the environment and Colombian minority ethnic groups

Transactional, Social, and Legal Aspects of Oil Exploration and Extraction in Colombia

In Colombia, as in many other countries with oil reserves potential, the government has sought to reduce the activity\u27s inherent high degree of un-certainty by shaping the legal and economic environment that foreign com-panies have to operate in, making it more profitable and attractive for them.16 This paper seeks to accurately represent this environment to the pro-spective investor, starting with the structures of the two basic transactions, referred to herein as modes , through which most commonly, foreign com-panies participate in the oil industry in Colombia, namely, the Standard As-sociation Mode ( S.A.M ) and the Risk Sharing Mode ( R.S.M. ).17 The contractual agreements corresponding to these modes are standardized and allow little tailoring to fit individual company needs. This part of the analysis will also include recent modifications to the foregoing modes, introduced to meet the government\u27s announced oil-policy objectives of increasing production, exploiting the existing reserves, and finding additional ones. In addition, a brief examination of the taxation re-gime will be followed by a discussion of the regulation implemented to pro- tect the environment and Colombian minority ethnic groups

Exploring alternatives to policy search

The field of Reinforcement Learning (RL) has been receiving much attention during the last few years as a new paradigm to solve complex problems. However, one of the main issues with the current state of the art is their computational cost. Compared with other paradigms such as Supervised learning, RL requires constant interaction with the environment, which is both expensive and hard to parallelize. In this work we explore a more scalable alternative to conventional RL through the use of Evolution Strategies (ES). This consists in iteratively modifying the current solution by adding Gaussian noise to it, evaluating these modifications, and use their score to guide the improvement of the solution. The advantage of ES lies on that creating and evaluating these modifications can be parallelized. After introducing the network routing scenario, we used it to compare how ES performed against PPO, a RL policy gradient method. Ultimately ES took advantage of increasing its number of workers to eventually overtake PPO, training faster while also generating better results overall. However, it was also clear that for this to occur ES must have access to a considerable amount of hardware resources, hence being viable only within high perfomance computing environments

Smart IoT Gateway For Heterogeneous Devices Interoperability

"(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works."The Internet of things (IoT) will interconnect a huge amount of devices, leading to a new way of interaction in the physical and virtual world, inspired by the idea of ubiquity, where all the objects around us, such as: sensors, automobiles, refrigerators, thermostats, industrial robots, tablets, smartphones, etc. could be connected anytime and anywhere. However, one of the main challenges that faces IoT is the high degree of heterogeneity in terms of communication capabilities of the devices, protocols, technologies or hardware. We focus on the implementation of a new Smart IoT Gateway designed to allow interconnection and interoperability between heterogeneous devices in the IoT. The proposed gateway offers significant advantages: (i) it enables connectivity of different protocols and traditional communication technologies (Ethernet) and wireless (ZigBee, Bluetooth, Wi-Fi); (ii) it uses a flexible protocol that translates all the data obtained from the different sensors into a uniform format, performing the analysis of the data obtained from the environment-based-rules related to the different types of sensors; (iii) it uses a lightweight and optimal protocol on the use of devices with limited resources for delivering information environment; and (iv) it provides local data storage for later use and analysis. Our proof of concept demonstrates the performance and capacity of the proposed Smart IoT Gateway is related with Active and Healthy Aging (AHA).Yacchirema-Vargas, DC.; Palau Salvador, CE. (2016). Smart IoT Gateway For Heterogeneous Devices Interoperability. IEEE Latin America Transactions. 14(8):3900-3906. https://doi.org/10.1109/TLA.2016.7786378S3900390614

The coalescent structure of Galton-Watson trees in varying environments

We investigate the genealogy of a sample of k particles chosen uniformly without replacement from a population alive at a large time n in a critical discrete-time Galton-Watson process in a varying environment (GWVE). We will show that subject to an explicit deterministic time-change involving only the mean and variances of the varying offspring distributions, the sample genealogy always converges to the same universal genealogical structure; it has the same tree topology as Kingman's coalescent, and the coalescent times of the k-1 pairwise mergers look like a mixture of independent identically distributed times. Our approach uses k spine particles and a change of measure $\mathbf{Q}_n^{(e,k, \theta)}$ under which the spines form a uniform sample without replacement at time n, as required, but additionally there is k-size biasing and discounting at rate $\theta$ by the population size at time n. We give a forward in time construction for the process with k spines under $\mathbf{Q}_n^{(e,k, \theta)}$ where the k size-biasing provides a great deal of structural independence that enables explicit calculations, and the discounting means that no additional offspring moment assumptions are required. Combining the special properties of $\mathbf{Q}_n^{(e,k, \theta)}$ together with the Yaglom theorem for GWVE, plus a suitable time-change that encodes variation within the environment, we then undo the k-size biasing and discounting to recover the limiting genealogy for a uniform sample of size k in the GWVE. Our work extends the spine techniques developed in Harris, et. al [Annals of Applied Probability, 2020] and complements recent work by Kersting [Proceedings of the Steklov Institute of Mathematics, 2022] which describes the genealogy of the entire extant population in the GWVE in the large time limi

LAS CONSECUENCIAS ECONÓMICAS DE UN NOMBRE ATÍPICO. EL CASO COLOMBIANO

Este artículo examina las consecuencias sobre los ingresos laborales de tener un nombre atípico para el caso colombiano. La primera parte del artículo muestra que los jóvenes, hijos de padres no educados, habitantes de zonas rurales y pertenecientes a minorías étnicas tienen una mayor probabilidad de tener un nombre atípico. La segunda parte muestra que el impacto de un nombre atípico sobre los salarios es sustancial (superior al 10%) y que el mismo es mucho mayor para las personas educadas que para los no educadas. Los resultados sugieren la existencia de mecanismos de transmisión intergeneracional alternativos a los tradicionales (restricciones de crédito, herencias, etc.). En Colombia, al menos, los nombres atípicos son no sólo una consecuencia de las desigualdades sociales, sino también una causa de las mismas.atípicos sin tocayo salarios exclusión social