Weak Convergence of Finite-Dimensional Distributions of Semimartingales to Distributions of Processes with Conditionally Independent Increments

1989 ◽  
pp. 361-496
Author(s):  
R. Sh. Liptser ◽  
A. N. Shiryayev
Keyword(s):  
Weak Convergence ◽  
Finite Dimensional ◽  
Independent Increments

scholarly journals Weak Convergence of Finite-Dimensional Distributions of the Number of Empty Boxes in the Bernoulli Sieve

2015 ◽  
Vol 59 (1) ◽  
pp. 87-113 ◽  
Author(s):  
A. M. Iksanov ◽  
A. V. Marynych ◽  
V. A. Vatutin
Keyword(s):  
Weak Convergence ◽  
Finite Dimensional

scholarly journals S-Subgradient Projection Methods with S-Subdifferential Functions for Nonconvex Split Feasibility Problems

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1517
Author(s):  
Jinzuo Chen ◽  
Mihai Postolache ◽  
Yonghong Yao
Keyword(s):  
Weak Convergence ◽  
Projection Method ◽  
Split Feasibility Problem ◽  
Projection Methods ◽  
Feasibility Problem ◽  
Split Feasibility Problems ◽  
Finite Dimensional ◽  
Subgradient Projection ◽  
Weak Convergence Theorem ◽  
Split Feasibility

In this paper, the original C Q algorithm, the relaxed C Q algorithm, the gradient projection method ( G P M ) algorithm, and the subgradient projection method ( S P M ) algorithm for the convex split feasibility problem are reviewed, and a renewed S P M algorithm with S-subdifferential functions to solve nonconvex split feasibility problems in finite dimensional spaces is suggested. The weak convergence theorem is established.

On the moments of some first-passage times

1985 ◽  
Vol 22 (02) ◽  
pp. 461-466
Author(s):  
Valeri T. Stefanov
Keyword(s):  
Continuous Function ◽  
Exponential Type ◽  
First Passage Time ◽  
Sequential Estimation ◽  
Passage Time ◽  
Positive Continuous Function ◽  
First Passage ◽  
Finite Dimensional ◽  
Independent Increments ◽  
Passage Times

Let {Xt } t≧0 (t may be discrete or continuous) be a random process whose finite-dimensional distributions are of exponential type. The first-passage time inf{t:Xt ≧f(t)}, where f(t) is a positive, continuous function, such that f(t)= o(t) as t↑∞, is considered. The problem of finiteness of its moments is solved for both the case that {Xt } t≧0 has stationary independent increments as well as the case in which no assumptions are made about stationarity and independence for the increments of the process. Applications to sequential estimation are also given.

scholarly journals Limit theorems for hitting times of 1-dimensional generalized diffusions

1998 ◽  
Vol 152 ◽  
pp. 1-37
Author(s):  
Matsuyo Tomisaki ◽  
Makoto Yamazato
Keyword(s):  
Limit Theorems ◽  
Bessel Functions ◽  
Diffusion Processes ◽  
Hitting Times ◽  
Finite Dimensional ◽  
Independent Increments ◽  
Starting Point ◽  
Self Similar ◽  
The Mean ◽  
The One

Abstract.Limit theorems are obtained for suitably normalized hitting times of single points for 1-dimensional generalized diffusion processes as the hitting points tend to boundaries under an assumption which is slightly stronger than that the existence of limits γ + 1 of the ratio of the mean and the variance of the hitting time. Laplace transforms of limit distributions are modifications of Bessel functions. Results are classified by the one parameter {γ}, each of which is the degree of corresponding Bessel function. In case the limit distribution is degenerate to one point, by changing the normalization, we obtain convergence to the normal distribution. Regarding the starting point as a time parameter, we obtain convergence in finite dimensional distributions to self-similar processes with independent increments under slightly stronger assumption.

A note on stochastic processes with independent increments taking values in an abelian group

1969 ◽  
Vol 6 (02) ◽  
pp. 449-452
Author(s):  
M.S. Bingham
Keyword(s):  
Abelian Group ◽  
Dimensional Euclidean Space ◽  
Time Interval ◽  
Time Points ◽  
Process With Independent Increments ◽  
Sample Paths ◽  
Finite Dimensional ◽  
Independent Increments ◽  
Processes With Independent Increments ◽  
Basic Ideas

It is well known that any stochastically continuous real valued stochastic process with independent increments defined on a compact time interval can be decomposed into a sum of independent processes, one of which is Gaussian with continuous sample paths, and the remainder of which have sample paths which are continuous except at a finite number of points with the discontinuities occurring at Poisson time points. The purpose of this note is to announce a proof of the above theorem in the case where the process takes values in an abelian group G. The detailed proof will appear elsewhere. The basic ideas of the proof in the case when G is finite dimensional Euclidean space are contained in Chapter VI of Gikhman and Skorohod (1965).

On the moments of some first-passage times

1985 ◽  
Vol 22 (2) ◽  
pp. 461-466
Author(s):  
Valeri T. Stefanov
Keyword(s):  
Continuous Function ◽  
Exponential Type ◽  
First Passage Time ◽  
Sequential Estimation ◽  
Passage Time ◽  
Positive Continuous Function ◽  
First Passage ◽  
Finite Dimensional ◽  
Independent Increments ◽  
Passage Times

Let {Xt}t≧0 (t may be discrete or continuous) be a random process whose finite-dimensional distributions are of exponential type. The first-passage time inf{t:Xt≧f(t)}, where f(t) is a positive, continuous function, such that f(t)= o(t) as t↑∞, is considered. The problem of finiteness of its moments is solved for both the case that {Xt}t≧0 has stationary independent increments as well as the case in which no assumptions are made about stationarity and independence for the increments of the process. Applications to sequential estimation are also given.

scholarly journals Convergence of Locally Square Integrable Martingales to a Continuous Local Martingale

2011 ◽  
Vol 2011 ◽  
pp. 1-34
Author(s):  
Andriy Yurachkivsky
Keyword(s):  
Gaussian Processes ◽  
Continuous Functions ◽  
Local Martingale ◽  
Initial Value ◽  
Finite Dimensional ◽  
Independent Increments ◽  
Integrable Martingale ◽  
Probability Spaces ◽  
Uniformly Continuous

Let for each be an -valued locally square integrable martingale w.r.t. a filtration (probability spaces may be different for different ). It is assumed that the discontinuities of are in a sense asymptotically small as and the relation holds for all , row vectors , and bounded uniformly continuous functions . Under these two principal assumptions and a number of technical ones, it is proved that the 's are asymptotically conditionally Gaussian processes with conditionally independent increments. If, moreover, the compound processes converge in distribution to some , then a sequence () converges in distribution to a continuous local martingale with initial value and quadratic characteristic , whose finite-dimensional distributions are explicitly expressed via those of .

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