Discrete-Time Martingales With Spatial Parameters

Zhang, Bo; Kannan, D.

doi:10.1081/sap-120014555

Cited by 2 publications

(7 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. Notice that in the proof of Lemma 3.1 (see Theorem 4.7 in [14]), we only needed the continuity. We can modify that proof to prove the conclusion of the present theorem.…”

Section: Remark 33 From the Sde (3) And The Proof Of Theorem 32 Wmentioning

confidence: 97%

“…We now state some basic assumptions needed to explore these stochastic properties and also quote a lemma from [14] that will be needed in our discussions infra. First, recall that for a C m -martingale F x k with parameter x ∈ ⊂ d its quadratic covariation is defined by…”

Section: Stochastic Propertiesmentioning

confidence: 99%

“…Some groundwork for this study has been done in our earlier work [5,14]; we will appeal to some of the results from them. The stochastic difference equations (abbreviated SdE) that we consider are of the following forms: for k = 0 1 2 ,…”

Section: Introductionmentioning

confidence: 99%

“…The following lemma, established in [14], is quoted here for ready reference. is a closed subspace of l .…”

Section: Introductionmentioning

confidence: 99%

“…So, we begin by introducing some sequence/function spaces that we used in [14], along with basic notations we need for this article.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Nonlinear Stochastic Difference Equations Driven by Martingales

Zhang¹,

Zhang²,

Kannan³

2005

Stochastic Analysis and Applications

Self Cite

View full text Add to dashboard Cite

We provide in this paper a systematic development of nonlinear stochastic difference equations driven by martingales (that depend on a spatial parameter); three such equations are considered. We begin with the existence and uniqueness of solutions and continue with the study of stochastic properties, such as the martingale and Markov properties, along with irreducibility and recurrence. We discuss in the final section the discrete-time flow and asymptotic flow properties of the solution process.

show abstract

“…Proof. Notice that in the proof of Lemma 3.1 (see Theorem 4.7 in [14]), we only needed the continuity. We can modify that proof to prove the conclusion of the present theorem.…”

Section: Remark 33 From the Sde (3) And The Proof Of Theorem 32 Wmentioning

confidence: 97%

Section: Stochastic Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The following lemma, established in [14], is quoted here for ready reference. is a closed subspace of l .…”

Section: Introductionmentioning

confidence: 99%

“…So, we begin by introducing some sequence/function spaces that we used in [14], along with basic notations we need for this article.…”

Section: Introductionmentioning

confidence: 99%