Stochastic process

About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.

Random Summation: Limit Theorems and Applications

Abstract: Examples Examples Related to Generalized Poisson Laws A Remarkable Formula of Queueing Theory Other Examples Doubling with Repair Mathematical Model A Limit Theorem for the Trouble-Free Performance Duration The Class of Limit Laws Some Properties of Limit Distributions Domains of Geometrical Attraction of the Laws from Class c Limit Theorems for "Growing" Random Sums A Transfer Theorem. Limit Laws Necessary and Sufficient Conditions for Convergence Convergence to Distributions from Identifiable Families Limit Theorems for Risk Processes Some Models of Financial Mathematics Rarefied Renewal Processes Limit Theorems for Random Sums in the Double Array Scheme Transfer Theorems. Limit Laws Converses of the Transfer Theorems Necessary and Sufficient Conditions for the Convergence of Random Sums of Independent Identically Distributed Random Variables More on Some Models of Financial Mathematics Limit Theorems for Supercritical Galton-Watson Processes Randomly Infinitely Divisible Distributions Mathematical Theory of Reliability Growth. A Bayesian Approach Bayesian Reliability Growth Models Conditionally Geometrical Models Conditionally Exponential Models Renewing Models Models with Independent Decrements of Volumes of Defective Sets Order-Statistics-Type (Mosaic) Reliability Growth Models Generalized Conditionally Exponential Models Statistical Prediction of Reliability by Renewing Models Statistical Prediction of Reliability by Order-Statistics-Type Models Appendix 1: Information Properties of Probability Distributions Mathematical Models of Information and Uncertainty Limit Theorems of Probability Theory and the Universal Principle of Non-Decrease of Uncertainty Appendix 2: Asymptotic Behavior of Generalized Doubly Stochastic Poisson Processes General Information on Doubly Stochastic Poisson Processes A General Limit Theorem for Superpositions of Random Processes Limit Theorem for Cox Processes Limit Theorems for Generalized Cox Processes Convergence Rate Estimates in Limit Theorems for Generalized Cox Processes Asymptotic Expansions for Generalized Cox Processes Estimates for the Concentration Functions of Generalized Cox Processes Bibliographical Commentary Index References

A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning.

Abstract: We explore a computationally efficient method of simulating realistic networks of neurons introduced by Knight, Manin, and Sirovich (1996) in which integrate-and-fire neurons are grouped into large populations of similar neurons. For each population, we form a probability density that represents the distribution of neurons over all possible states. The populations are coupled via stochastic synapses in which the conductance of a neuron is modulated according to the firing rates of its presynaptic populations. The evolution equation for each of these probability densities is a partial differential-integral equation, which we solve numerically. Results obtained for several example networks are tested against conventional computations for groups of individual neurons. We apply this approach to modeling orientation tuning in the visual cortex. Our population density model is based on the recurrent feedback model of a hypercolumn in cat visual cortex of Somers et al. (1995). We simulate the response to oriented flashed bars. As in the Somers model, a weak orientation bias provided by feed-forward lateral geniculate input is transformed by intracortical circuitry into sharper orientation tuning that is independent of stimulus contrast. The population density approach appears to be a viable method for simulating large neural networks. Its computational efficiency overcomes some of the restrictions imposed by computation time in individual neuron simulations, allowing one to build more complex networks and to explore parameter space more easily. The method produces smooth rate functions with one pass of the stimulus and does not require signal averaging. At the same time, this model captures the dynamics of single-neuron activity that are missed in simple firing-rate models.

ML estimation of a stochastic linear system with the EM algorithm and its application to speech recognition

Abstract: A nontraditional approach to the problem of estimating the parameters of a stochastic linear system is presented. The method is based on the expectation-maximization algorithm and can be considered as the continuous analog of the Baum-Welch estimation algorithm for hidden Markov models. The algorithm is used for training the parameters of a dynamical system model that is proposed for better representing the spectral dynamics of speech for recognition. It is assumed that the observed feature vectors of a phone segment are the output of a stochastic linear dynamical system, and it is shown how the evolution of the dynamics as a function of the segment length can be modeled using alternative assumptions. A phoneme classification task using the TIMIT database demonstrates that the approach is the first effective use of an explicit model for statistical dependence between frames of speech. >

The effect of execution policies on the semantics and analysis of stochastic Petri nets

Abstract: Petri nets in which random delays are associated with atomic transitions are defined in a comprehensive framework that contains most of the models already proposed in the literature. To include generally distributed firing times into the model one must specify the way in which the next transition to fire is chosen, and how the model keeps track of its past history; this set of specifications is called an execution policy. A discussion is presented of the impact that different execution policies have on semantics of the mode, as well as the characteristics of the stochastic process associated with each of these policies. When the execution policy is completely specified by the transition with the minimum delay (race policy) and the firing distributions are of the phase type, an algorithm is provided that automatically converts the stochastic process into a continuous time homogeneous Markov chain. An execution policy based on the choice of the next transition to fire independently of the associated delay (preselection policy) is introduced, and its semantics is discussed together with possible implementation strategies. >