New Results in Branching Processes using Stochastic Approximation Techniques
We consider various types of continuous-time two-type population size-dependent Markov Branching process. The offspring distribution can depend on current population (i.e., population alive at the given time) and or on the total population (past and current). Using the techniques of stochastic approximation, we create an ODE based framework to study a general class of such processes. Our particular focus is on time-asymptotic proportion of the two populations. We also provide ODEs whose solutions can approximate certain normalized trajectories of the branching processes. In addition to extending the analysis of several existing BPs, we analyse three new variants: branching process with attack and acquisition, branching process with proportion dependent offsprings (even after long run) and super to sub-critical saturated branching process. We use these three new variants to study competition in viral markets, fake news control mechanism and saturation in viral markets.
Veeraruna Kavitha is currently an Associate Professor at IEOR, IIT Bombay, India. She received her Ph.D. degrees from Indian Institute of Science (IISc), Bangalore. She was an NBHM (National Board for Higher Mathematics) post-doctoral fellow at Tata Institute of Fundamental Research (TIFR), Bangalore, during 2007-08. Between 2008-2011 she was a post-doctoral researcher with MAESTRO, INRIA, Sophia Antipolis, France and LIA, University of Avignon, France. Her research interests span stochastic processes, performance analysis, game theory, optimal control and optimization, Markov decision processes and wireless networks.