论文信息 - Chaos expansion methods of stochastic processes for Malliavin-type equations

Chaos expansion methods of stochastic processes for Malliavin-type equations

Abstract In this short survey we present the application of the Askey-scheme of orthogonal polynomials to define several discrete and continuous distribution types in frame-work of T. Hidaʼs white noise analysis. The results are applied to define fractional versions of the distributions and to solve stochastic differential equations involving the Malliavin derivative, Skorokhod integral and Ornstein-Uhlenbeck operator.

Tijana Levajkovic | Dora Selesi | T. Levajković | D. Seleši | Dora Seleši

[1] B. Rozovskii,et al. On generalized Malliavin calculus , 2012 .

[2] S. Pilipovic,et al. EXPANSION THEOREMS FOR GENERALIZED RANDOM PROCESSES, WICK PRODUCTS AND APPLICATIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS , 2007 .

[3] W. Schoutens. Stochastic processes and orthogonal polynomials , 2000 .

[4] Bernt Øksendal,et al. Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach , 1996 .

[5] Bernt Øksendal,et al. WHITE NOISE. AN INFINITE DIMENSIONAL CALCULUS , 1995 .

[6] Rene F. Swarttouw,et al. Orthogonal polynomials , 2020, NIST Handbook of Mathematical Functions.

[7] Chaos expansion methods for stochastic differential equations involving the Malliavin derivative, Part II , 2011 .