Results 141 to 150 of about 17,630 (184)

Two-Parameter Martingales and Their Properties

2013
This chapter provides well-known results concerning the properties of two-parametric martingales and stochastic integration on the plane. We begin with the auxiliary chapter, which also contains some facts which are of independent interest. Our standard references for the results below are [20–24, 40, 42, 44, 47, 48, 65, 71].
Pavel S. Knopov, Olena N. Deriyeva
openaire   +1 more source

On integral representations of two-parameter martingales

rose, 1993
Summary: Sufficient conditions under which every square integrable two-parameter martingale \(N\) can be represented in the form \(N= \int_{R_z} \varphi dM+ \iint_{R_z\times R_z} \psi dM dM\), where \(M\) is a given continuous 4-integrable strong martingale, are derived.
openaire   +1 more source

Exponential estimates for two-parameter martingales

Ukrainian Mathematical Journal, 1988
The paper is devoted to the exponential estimates for distributions of continuous two-parameter martingales. More precisely, the probability \(P\{\sup_{t\leq T}| x_ t| \geq \alpha T_ 1T_ 2\}\) is estimated by exponentials. The estimates are given for those martingales \(x_ t\) that have ``one-parameter'' square functions of bounded growth: \(^ i_ t\leq
openaire   +1 more source

Some Laws of the Iterated Logarithm for Two Parameter Martingales

Journal of Theoretical Probability, 1999
The author obtains some laws of the iterated logarithm for two parameter martingales \(X=\{X_t: t\in N^2\}\) where \(N\) denotes the set of integers. Put \({\mathcal F}_t= \sigma\{X_s:s\leq t\}\), \(t\in N^2\), where the inequality \(s\leq t\) is meant to hold componentwise, and let \({\mathcal F}_1^{(m)}(0-)\) \((m=0,1,\dots)\) denote the \(\sigma ...
openaire   +2 more sources

On a martingale characterization of two-parameter Wiener process

Statistics & Probability Letters, 1990
Abstract A generalization of martingales, named string-martingales in this paper, is introduced for two-dimensional-parameter processes. The two-parameter standard Wiener process is then characterised as a strong-martingale with continuous paths, and an additional property which states that a sort of quadratic variation of the process is ...
openaire   +1 more source

Two parameter smooth martingales on the Wiener space

Acta Mathematica Sinica, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Weak atomic decomposition of B-valued martingales with two-parameters

Acta Mathematica Hungarica, 2010
\textit{R. Cheng} and \textit{G. Shixin} [Acta Math. Hung. 93, No.~1--2, 7--25 (2001; Zbl 1012.60048)] obtained atomic decompositions for B-valued martingales in the two-parameter case. In this paper, the authors define some weak atoms and prove atomic decomposition theorems in weak Hardy spaces.
Li, Y. F., Liu, P. D.
openaire   +1 more source

The transformation theorem for two-parameter pure jump martingales

Probability Theory and Related Fields, 1991
Let M be a martingale of pure jump type, i.e. the compensation of the process describing the total of the point jumps of M in the plane. M can be uniformly approximated by martingales of bounded variation jumping only on finitely many axial parallel lines.
openaire   +2 more sources

Proof of existence theorems for the two-parameter martingale problem

Siberian Mathematical Journal, 1995
Following \textit{D. W. Stroock} and \textit{S. R. S. Varadhan} [Commun. Pure Appl. Math. 22, 345--400 (1969; Zbl 0167.43903)], the author considers existence theorems for two-parameter martingale problem. Briefly, the measure \(P\) is called a solution of martingale problem for \((z_0,x_0,a,b)\) if \(P\{x(z,\cdot)=x_0(z)\), \(z\in\partial I_{z_0}\}=1\)
openaire   +1 more source

Planar seminartingales obtained by transformations of two-parameter martingales

1989
In this paper we study the weak local submartingale property and the quasimartingale property of processes obtained by the composition of a two-parameter continuous martingale by c2-functions whose second derivative is convex.
Nguyen Minh Duc, D. Nualart, M. Sanz
openaire   +1 more source