| 1. |
- Bock, Wolfgang, et al.
(författare)
-
A white noise approach to phase space Feynman path integrals
- 2012
-
Ingår i: Theory of Probability and Mathematical Statistics. - : Tara Shevchenko National University Kyiv. - 0094-9000 .- 1547-7363. ; 85, s. 7-22
-
Tidskriftsartikel (refereegranskat)abstract
- The concepts of phase space Feynman integrals in White Noise Analysis are established. As an example the harmonic oscillator is treated. The approach perfectly reproduces the right physics. I.e., solutions to the Schrodinger equation are obtained and the canonical commutation relations are satisfied. The later can be shown, since we not only construct the integral but rather the Feynman integrand and the corresponding generating functional.
|
|
| 2. |
- Silvestrov, Dmitrii, et al.
(författare)
-
Convergence of option rewards for Markov type price processes modulated by stochastic indices. II
- 2010
-
Ingår i: Theory of Probability and Mathematical Statistics. - Providence, R.I. : American Mathematical Society. - 0094-9000 .- 1547-7363. ; 80, s. 153-172
-
Tidskriftsartikel (refereegranskat)abstract
- A general price process represented by a two-component Markov process is considered. Its first component is interpreted as a price process and the second one as an index process modulating the price component. American type options with pay-off functions, which admit power type upper bounds, are studied. Both the transition characteristics of the price processes and the pay-off functions are assumed to depend on a perturbation parameter δ ≥ 0 and to converge to the corresponding limit characteristics as δ → 0. In the first part of the paper, asymptotically uniform skeleton approximations connecting reward functionals for continuous and discrete time models were given. In the second part of the paper, these skeleton approximations are used for getting results about the convergence of reward functionals for American type options for perturbed price processes with discrete and continuous time. Examples related to modulated exponential price processes with independent increments are given.
|
|
| 3. |
- Silvestrov, Dmitrii S., et al.
(författare)
-
Convergence of option rewards for multivariate price processes
- 2012
-
Ingår i: Theory of probability and mathematical statistics. - 1547-7363 .- 0094-9000. ; 85, s. 115-131
-
Tidskriftsartikel (refereegranskat)abstract
- American type options with general payoff functions possessing polynomial rate of growth are considered for multivariate Markov price processes. Convergence results for optimal reward functionals of American type options for perturbed multivariate Markov processes are presented. These results are applied to approximation tree type algorithms for American type options for exponential multivariate Brownian price processes and mean-reverse price processes used to model stochastic dynamics of energy prices.
|
|
| 4. |
- Malyarenko, Anatoliy, 1957-, et al.
(författare)
-
EDITORIAL
- 2021
-
Ingår i: THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS. - : TARAS SHEVCHENKO NATL UNIV KYIV, FAC MECH & MATH. - 0094-9000 .- 1547-7363. ; 105, s. 1-2
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
|
|
| 5. |
- Silvestrov, Dmitrii, 1947-
(författare)
-
Convergence in distribution for randomly stopped random fields
- 2021
-
Ingår i: Theory of Probability and Mathematical Statistics. - Kyiv : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; 105, s. 137-149
-
Tidskriftsartikel (refereegranskat)abstract
- Let X and Y be two complete, separable, metric spaces, xi(epsilon)(x), x is an element of X and nu(epsilon) be, for every epsilon is an element of[0, 1], respectively, a random field taking values in space Y and a random variable taking values in space X. We present general conditions for convergence in distribution for random variables xi(epsilon)(nu(epsilon)) that is the conditions insuring holding of relation, xi(epsilon)(nu(epsilon)) d ->xi(0)(nu(0)) as epsilon -> 0.
|
|
| 6. |
- Alfelt, Gustav, 1985-
(författare)
-
Closed-form estimator for the matrix-variate Gamma distribution
- 2020
-
Ingår i: Theory of Probability and Mathematical Statistics. - : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; 103, s. 137-154
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a novel closed-form estimator for the parameters of the matrix-variate gamma distribution. The estimator relies on the moments of a transformation of the observed matrices, and is compared to the maximum likelihood estimator (MLE) through a simulation study. The study reveals that when the underlying scale matrix parameter is ill-conditioned, or when the shape parameter is close to its lower bound, the suggested estimator outperforms the MLE, in terms of sample estimation error. In addition, since the suggested estimator is closed-form, it does not require numerical optimization as the MLE does, thus needing shorter computation time and is furthermore not subject to start value sensitivity or convergence issues. Finally, regarding the case of general parameter values, using the proposed estimator as start value in the optimization procedure of the MLE is shown to substantially reduce computation time, in comparison to using arbitrary start values.
|
|
| 7. |
- Alfelt, Gustav
(författare)
-
Stein-Haff Identity for the Exponential Family
- 2018
-
Ingår i: Theory of Probability and Mathematical Statistics. - : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; 99, s. 5-17
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, the Stein-Haff identity is established for positive-definite and symmetric random matrices belonging to the exponential family. The identity is then applied to the matrix-variate gamma distribution, and an estimator that dominates the maximum likelihood estimator in terms of Stein's loss is obtained. Finally, a simulation study is conducted in order to support the theoretical results.
|
|
| 8. |
- Avelin, Benny, 1984-, et al.
(författare)
-
ON EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
- 2021
-
Ingår i: THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS. - : TARAS SHEVCHENKO NATL UNIV KYIV, FAC MECH & MATH. - 0094-9000 .- 1547-7363. ; 104, s. 49-60
-
Tidskriftsartikel (refereegranskat)abstract
- In this article we consider existence and uniqueness of the solutions to a large class of stochastic partial differential equations of the form partial derivative(t)u = L(x)u+ b(t, u)+ s(t, u) (over dot(W)), driven by a Gaussian noise. W, white in time, and with spatial correlations given by a generic covariance gamma. We provide natural conditions under which classical Picard iteration procedure provides a unique solution. We illustrate the applicability of our general result by providing several interesting particular choices for the operator L-x under which our existence and uniqueness results hold. In particular, we show that Dalang condition given in [5] is sufficient in the case of many parabolic and hypoelliptic operators L-x.
|
|
| 9. |
- Bock, Wolfgang, et al.
(författare)
-
Stochastic analysis for vector-valued generalized grey Brownian motion
- 2023
-
Ingår i: Theory Probability and Mathematical Statistics. - : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; :108, s. 1-27
-
Tidskriftsartikel (refereegranskat)abstract
- In this article, we show that the standard vector-valued generalization of a generalized grey Brownian motion (ggBm) has independent components if and only if it is a fractional Brownian motion. In order to extend ggBm with independent components, we introduce a vector-valued generalized grey Brownian motion (vggBm). The characteristic function of the corresponding measure is introduced as the product of the characteristic functions of the one-dimensional case. We show that for this measure, the Appell system and a calculus of generalized functions or distributions are accessible. We characterize these distributions with suitable transformations and give a d-dimensional Donsker’s delta function as an example for such distributions. From there, we show the existence of local times and self-intersection local times of vggBm as distributions under some constraints, and compute their corresponding generalized expectations. At the end, we solve a system of linear SDEs driven by a vggBm noise in d dimensions.
|
|
| 10. |
- Bodnar, Olha, senior lecturer, 1979-
(författare)
-
Non-Informative Bayesian Inference for Heterogeneity in a Generalized Marginal Random Effects Meta-Analysis
- 2020
-
Ingår i: Theory of Probability and Mathematical Statistics. - : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; 100, s. 7-23
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper an objective Bayesian inference is proposed for the heterogeneity parameter in a generalized marginal random effects model. Models of this kind are widely used in meta-analysis and in inter-laboratory comparisons. Under the assumption of elliptically contoured distributions, a reference prior for the model parameters is obtained and the analytical expression of the corresponding posterior is derived. We also state necessary conditions for the resulting posterior to be proper and for the existence of its first two moments. The obtained general theoretical results are illustrated for three popular families of elliptically contoured distributions: normal distribution, t-distribution, and Laplace distribution.
|
|
