Work

Transportation cost-information inequality for non-linear time-fractional stochastic heat equation driven by space–time white noise

Year: 2025

Type: article

Abstract: We establish transportation cost-information inequalities T 2 ( C ) for solutions of nonlinear stochastic partial differential equation of fractional order in both space and time variables with deterministic and bounded initial conditions: ∂ t β u ( t , x ) + ( − Δ ) α / 2 u ( t , x ) = I t γ σ ( u ( t , x ) ) W ̇ ( t , x ) in ( 0 , ∞ ) × R d , where α > 0 , β ∈ ( 0 , 2 ] , γ ≥ 0 , ∂ t β is the Caputo fractional derivative, − ( − Δ ) α / 2 is the fractional/power of Laplacian, I t γ is the Riemann–Liouville integral operator, W ̇ ( t , x ) is a space–time white noise, and σ : R → R is a bounded and Lipschitz function. Since the space variable is defined on the unbounded domain R d , the inequalities are proved under a weighted L 2 -norm in the spatial domain.

Source: Statistics & Probability Letters

DOI: 10.1016/j.spl.2025.110519

Authors: Ruinan Li, Yumeng Li

Institutions: Shanghai University of International Business and Economics, Zhongnan University of Economics and Law

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,180

Funder: National Natural Science Foundation of China