The linear stochastic heat equation with Hermite noise

被引：10

作者：

Slaoui, Meryem ^{[1
]}

Tudor, C. A. ^{[1
]}

机构：

[1] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2019年 / 22卷 / 03期

关键词：

Wiener chaos; stochastic heat equation; Hermite process; Rosenblatt process; fractional Brownian motion; multiple stochastic integrals; cumulants; self-similarity; multiparameter stochastic processes; SELF-SIMILAR PROCESSES; EVOLUTION EQUATIONS; WIENER INTEGRALS; RANDOM-FIELD; RESPECT;

D O I：

10.1142/S021902571950022X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze the solution to the linear stochastic heat equation driven by a multiparameter Hermite process of order q >= 1. This solution is an element of the qth Wiener chaos. We discuss various properties of the solution, such as the necessary and sufficient condition for its existence, self-similarity, alpha-variation and regularity of its sample paths. We will also focus on the probability distribution of the solution, which is non-Gaussian when q >= 2.

引用

页数：23

共 29 条

[1] Structure of the third moment of the generalized Rosenblatt distribution [J].

Bai, Shuyang ;

Taqqu, Murad S. .

STATISTICS & PROBABILITY LETTERS, 2014, 94 :144-152

[2] The stochastic wave equation with fractional noise: A random field approach [J].

Balan, Raluca M. ;

Tudor, Ciprian A. .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2010, 120 (12) :2468-2494

[3] Dissipative Stochastic Evolution Equations Driven by General Gaussian and Non-Gaussian Noise [J].

Bonaccorsi, S. ;

Tudor, C. A. .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2011, 23 (04) :791-816

[4] Wiener integrals with respect to the Hermite random field and applications to the wave equation [J].

Clarke De la Cerda, Jorge ;

Tudor, Ciprian A. .

COLLECTANEA MATHEMATICA, 2014, 65 (03) :341-356

[5] WAVELET ESTIMATION OF THE LONG MEMORY PARAMETER FOR HERMITE POLYNOMIAL OF GAUSSIAN PROCESSES [J].

Clausel, M. ;

Roueff, F. ;

Taqqu, M. S. ;

Tudor, C. .

ESAIM-PROBABILITY AND STATISTICS, 2014, 18 :42-76

[6] Limiting measure and stationarity of solutions to stochastic evolution equations with Volterra noise [J].

Coupek, P. .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2018, 36 (03) :393-412

[7] Stochastic evolution equations with Volterra noise [J].

Coupek, P. ;

Maslowski, B. .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2017, 127 (03) :877-900

[8] Lp-valued stochastic convolution integral driven by Volterra noise [J].

Coupek, Petr ;

Maslowski, Bohdan ;

Ondrejat, Martin .

STOCHASTICS AND DYNAMICS, 2018, 18 (06)

[9]

Diu Tran T. T., 2017, PREPRINT

[10] GAUSSIAN AND THEIR SUBORDINATED SELF-SIMILAR RANDOM GENERALIZED FIELDS [J].

DOBRUSHIN, RL .

ANNALS OF PROBABILITY, 1979, 7 (01) :1-28

← 1 2 3 →