Stochastic Modeling of Compact Binary Coalescences for Gravitational Wave Analysis

Abstract

Aims: To develop a stochastic mathematical framework for modeling gravitational wave signals from Compact Binary Coalescences (CBCs), incorporating uncertainties in mass and spin evolution and improving signal detection and parameter estimation. Study Design: A simulation-based theoretical study using a stochastic approach to enhance the modeling of gravitational wave signals. Methodology: The model integrates the inspiral-merger-ringdown (IMR) waveform with stochastic differential equations (SDEs) to represent uncertainties in component evolution due to astrophysical and numerical factors. Monte Carlo simulations are used to analyze probabilistic behavior in mass and spin dynamics. Kalman filtering is applied for tracking evolving parameters in noisy data, while matched filtering and Bayesian inference are employed for signal extraction and posterior parameter estimation. All simulations are implemented in MATLAB. Results: Simulations show that spin parameters are more sensitive to stochastic fluctuations than mass. Kalman filtering accurately tracks hidden parameters under noisy conditions. Matched filtering effectively identifies weak gravitational wave signals, and Bayesian inference provides well-centered Gaussian posterior distributions, supporting reliable parameter estimation. Conclusion: The proposed stochastic framework enhances the realism and robustness of gravitational wave modeling from CBCs. By combining stochastic dynamics with advanced filtering and inference techniques, the study demonstrates a comprehensive approach for analyzing signals under uncertain conditions, offering valuable insights for future gravitational wave detection and analysis efforts.