Results 141 to 150 of about 36,708 (189)

Stopping a two parameter weak martingale

Probability Theory and Related Fields, 1987
This paper deals with the following problem: Given a two parameter stochastic process, under what conditions is it possible to stop the process at any stopping line? It is shown that the class of stoppable processes is strictly larger than the class of two parameter integrators.
Merzbach, Ely, Zakai, Moshe
openaire   +1 more source

Two-parameter martingales

Russian Mathematical Surveys, 1982
CONTENTSIntroduction § 1. General definitions § 2. Some examples § 3. Inequalities § 4. Martingales of a continuous argument § 5. The characteristics of martingales § 6.
openaire   +3 more sources

Different kinds of two-parameter martingales

Israel Journal of Mathematics, 1985
Different kinds of two-parameter martingales were progressively introduced by several authors on a two-parameter stochastic basis (\(\Omega\),\({\mathcal F},P,({\mathcal F}_{st})_{s,t\geq 0}):\) weak martingales, i-martingales, strong martingales, martingales with orthogonal increments, path-invariant martingales and direction-invariant martingales ...
Merzbach, Ely, Nualart, David
openaire   +2 more sources

Exponential inequalities for two-parameter martingales

Statistics & Probability Letters, 2001
The authors prove the following exponential inequality for two-parameter martingales: Let \(M=\{M_z, z\in\mathbb{R}^2_+\}\) be a two-parameter martingale whose quadratic variation \(([M]_z,\;z\in\mathbb{R}^2_+)\) is bounded by an increasing function \(f(z)\).
Moret, Sílvia, Nualart, David
openaire   +1 more source

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