Probability and Mathematical Statistics, 37, z. 1, 2017, ss.216

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In memoriam: Czesław Ryll-Nardzewski’s contributions to probability theory

DOI: http://dx.doi.org/10.19195/0208-4147.37.1.1

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Ryll-Nardzewski, biography, probability theory

Tangential existence and comparison, with applications to single and multiple integration

DOI: http://dx.doi.org/10.19195/0208-4147.37.1.2

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Tangential processes, local characteristics, conditional symmetry, marked point processes, compensators, stochastic integration, multiple stochastic integrals.

Intrinsic compound kernel estimates for the transition probability density of Lévy-type processes and their applications

DOI: http://dx.doi.org/10.19195/0208-4147.37.1.3

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Transition probability density, Lévytype processes, pseudo-differential operator, generator, Levi’s parametrix method.

Cramér type large deviations for trimmed L-statistics

DOI: http://dx.doi.org/10.19195/0208-4147.37.1.4

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Trimmed L-statistics, central limit theorem, large deviations, moderate deviations

Green function for gradient perturbation of unimodal Lévy processes

DOI: http://dx.doi.org/10.19195/0208-4147.37.1.5

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Unimodal Lévy process, heat kernel, smooth domain, Green function, gradient perturbation

Exponential rate of convergence independent of the dimension in a mean-field system of particles

DOI: http://dx.doi.org/10.19195/0208-4147.37.1.6

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Mean-field model, Poincaré inequality, transportation inequality, high dimension

Functional limit theorems in Hölder space for residuals of nearly nonstationary AR(1) process

DOI: http://dx.doi.org/10.19195/0208-4147.37.1.7

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Nearly nonstationary process, residuals, Hölderian functional limit theorems, epidemic change

Strong law of large numbers for random variables with multidimensional indices

DOI: http://dx.doi.org/10.19195/0208-4147.37.1.8

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Strong law of large numbers, sums of random fields, multidimensional index

Weak convergence of a numerical scheme for stochastic differential equations

DOI: http://dx.doi.org/10.19195/0208-4147.37.1.9

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Numerical methods, round-off error, stochastic differential equations, weak convergence

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