Students t distribution and related stochastic processes grigelionis bronius
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Theory of Probability and its Applications, 7 1 :24—57,???? The influence of central observations on discrimination among multivariate extremal models. Exponential bounds for smooth fields. On the strong law of large numbers for second order stationary processes and sequences. We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. On the minimax estimation problem of a fractional derivative.

Original Russian article in Teor. Theory of Probability and its Applications, 20 3 :648—652,???? On extrapolation of a random field satisfying the wave equation. Optimal multiple stopping with sum-payoff. We consider the problem of parameter estimation for an ergodic diffusion with the symmetric scaled Student invariant distribution, where the spectral representation of the transition density is given in terms of the finite number of polynomial eigenfunctions Routh—Romanovski polynomials and absolutely continuous spectrum of the negative infinitesimal generator of observed diffusion. Theory of Probability and its Applications, 37 1 :142—145, March 1993. Theory of Probability and its Applications, 31 4 : 693—697,???? It offers a compendium of most distributionfunctions used by communication engineers, queuing theoryspecialists, signal processing engineers, biomedical engineers,physicists, and students.

Theory of Probability and its Applications, 59 4 :590—610,???? In addition, it reviews sample function properties and spectral representations for stationary processes and fields, including a portion on stationary point processes. Theory of Probability and its Applications, 20 1 :169—174,???? Limit theorem for diffusion processes with switchings. Theory of Probability and its Applications, 52 3 :439—455,???? Theory of Probability and its Applications, 11 2 :311—313,???? Original Russian article in Teor. On the average number of crossings of a level by the sample functions of a stochastic process. Theory of Probability and its Applications, 36 3 :594—596, September 1992. On the joint distribution of the first exit time and exit value for homogeneous processes with independent increments. Next, we clarify a higher order property of the moment type estimator by the Edgeworth expansion of the distribution function.

Theory of Probability and its Applications, 28 2 :337—350,???? Independent linear statistics on a-adic solenoids. On the expected number of real zeros of random polynomials I. Nash equilibrium in a game of calibration. Theory of Probability and its Applications, 17 3 :379—400,???? Boundary-value problems for systems of stochastic partial differential equations. Theory of Probability and its Applications, 22 1 :133—140,???? An inequality for a multidimensional characteristic function. Theory of Probability and its Applications, 13 3 :421—437,???? Theory of Probability and its Applications, 59 4 : 684—693,???? Theory of Probability and its Applications, 34 3 :554—555,???? Despite all this experimental progress, and despite the wide interest in gaining a better understanding of the behavior of individual neurons and of systems of neurons, there has been little success in the efforts to develop stochastic mathematical models capable of reflecting and helping to predict neuronal activity.

Theory of Probability and its Applications, 21 3 : 614—620,???? In particular, we provide simple criteria for the stability or instability of the corresponding stock price model, and we give explicit formulae for the invariant distributions in the recurrent case. Theory of Probability and its Applications, 47 3 :518—526, September 2003. Theory of Probability and its Applications, 8 2 :157—164,???? Estimation in Gaussian white noise using a finite number of linear statistics. Theory of Probability and its Applications, 54 1 :140—150,???? Theory of Probability and its Applications, 44 1 :201— 217, March 2000. Theory of Probability and its Applications, 55 2 :198— 224,???? Theory of Probability and its Applications, 20 3 : 641—644,???? On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements. Original Russian article in Teor. The rate of convergence of spectra of sample covariance matrices.

Maximum likelihood estimator and Kullback— Leibler information in misspecified Markov chain models. On joint distribution of random variables with given cross conditional distributions: Discrete case. Theory of Probability and its Applications, 19 2 :267—277,???? Theory of Probability and its Applications, 45 1 :133—135, March 2001. We have tried to maintain a b- ance in presenting advanced but understandable material that sparks an interest and challenges students, without the discouragement that often comes as a consequence of not understanding the material. Theory of Probability and its Applications, 27 3 :609—613,???? Theory of Probability and its Applications, 16 2 :228—248,???? On weighted M -estimates in nonlinear regression. Theory of Probability and its Applications, 16 3 :528—533,???? Author by : Richard M. Theory of Probability and its Applications, 28 3 :573—584,???? Theory of Probability and its Applications, 27 4 :780—794,???? A remark on probability distributions of class L.

Theory of Probability and its Applications, 48 3 :535—541, September 2004. Estimation problems for coefficients of stochastic partial differential equations. Theory of Probability and its Applications, 48 1 :93— 107, March 2004. Theory of Probability and its Applications, 18 3 :531—545,???? One effective method for active learning is, after at most 20 minutes of lecture, to assign a small example problem for the students to work and one important tool that the instructor can utilize is the computer. Theory of Probability and its Applications, 42 3 :405—415,???? A representation for some martingales. The theory is applied to a model with proportional decay of the postsynaptic potential and to the equivalent circuit of the membrane.

Theory of Probability and its Applications, 12 2 :297—301,???? It is the selfless effort of sev eral people that brought about these conferences. Theory of Probability and its Applications, 18 3 :442—453,???? Theory of Probability and its Applications, 33 3 :552—556,???? Spectral decomposition of the transition density of such a Markov process is presented in terms of a finite number of discrete eigenfunctions Bessel polynomials and eigenfunctions related to a continuous part of the spectrum of the negative infinitesimal generator of reciprocal gamma diffusion. . Diffusion models with linear drift and a known and prespecified marginal distribution are studied, and the diffusion coefficients corresponding to a large number of common probability distributions are found explicitly. On duality principle for hedging strategies in diffusion models. Theory of Probability and its Applications, 43 3 :370— 387, September 1999.

Original Russian article in Teor. Theory of Probability and its Applications, 20 3 :612—622,???? Conditions for local convergence of recursive stochastic procedures. Weak convergence of the empirical process and the rescaled empirical distribution function in the Skorokhod product space. We do not address the interesting questions of how networks of interconnected neurons behave. Theory of Probability and its Applications, 50 4 :659—662, January 2006. On the shape of trajectories of Gaussian processes having large massive excursions. The Skitovich— Darmois theorem for discrete periodic Abelian groups.