Work

Existence and uniqueness of stochastic PDEs associated with the forward equations: An approach using alternate norms

Year: 2025

Type: article

Abstract: In this paper, we consider a class of stochastic PDEs and associated PDEs with regular initial conditions. Here, the diffusion coefficient operator [Formula: see text] and drift coefficient operator [Formula: see text] are certain partial differential operators involving multiplication by smooth functions and are of the order one and two respectively, and in special cases are associated with finite dimensional diffusion processes. This PDE also includes Kolmogorov’s forward equation (Fokker–Planck equation) as a special case. We first prove a Monotonicity inequality for the pair [Formula: see text] and using this inequality, we obtain the existence and uniqueness of strong solutions to the Stochastic PDE and the PDE. In addition, a stochastic representation for the solution to the PDE is also established.

Source: Infinite Dimensional Analysis Quantum Probability and Related Topics

DOI: 10.1142/s0219025725500079

Authors: Suprio Bhar, Rajeev Bhaskaran, Arvind Kumar Nath

Institutions: Indian Institute of Technology Kanpur, Indian Institute of Science Education and Research Thiruvananthapuram

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: University Grants Commission, Science and Engineering Research Board, UGC-DAE Consortium for Scientific Research, University Grants Commission

Award: G6550901161