Resolvent stochastic processes

IF 0.7 4区数学 Q2 MATHEMATICS St Petersburg Mathematical Journal Pub Date : 2024-04-12 DOI:10.1090/spmj/1797

I. Ibragimov, N. Smorodina, M. Faddeev

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引用次数: 0

Abstract

A family r λ r_\lambda , λ ∈ C \lambda \in \mathbb {C} , of complex stochastic processes is introduced, which makes it possible to construct a probabilistic representation for the resolvent of the operator − 1 2 d 2 d x 2 -\frac {1}{2}\frac {d^2}{dx^2} . For λ = 0 \lambda =0 , the process r λ r_\lambda coincides with the Brownian local time process.

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溶剂随机过程

在 \mathbb {C} 中引入了一个系列 r λ r_\lambda , λ ∈ C \lambda \。引入了复杂随机过程，这使得为算子 - 1 2 d 2 d x 2 -\frac {1}{2}\frac {d^2}{dx^2}的解析量构建概率表示成为可能。对于 λ = 0 \lambda =0，过程 r λ r_\lambda 与布朗局部时间过程重合。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

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