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<p>In this manuscript, we investigate a class of fractional stochastic differential equations driven by time-changed Brownian motion (TCBM) with impulsive condition. The existence and uniqueness results are proved in the finite-dimensional space via fixed-point approach. Further, some novel sufficient conditions ensuring the Ulam-Hyer’s Rassias stability (UHRS) in means square by employing the retarded Gronwall-like inequalities. Illustrative examples are provide to obtain theoretical results. Inspired by the interaction between reduced form and structural credit models, we suggest modeling the firm value process as a time-varying Bm that could incorporate stochastic volatility effects and leaps as well as to examine the first passage issue for these kinds of procedures. Utilizing time change structure, the first passage problem for stochastic processes reveals that the distribution functions are efficiently calculable in a variety of practical instances.</p>

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Ulam-Hyers-Rassias stability for fractional stochastic impulsive differential equations driven by time-changed Brownian motion followed by credit risk modeling

  • 期刊论文

  • 发表日期：

    2025年5月8日

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  • Dimplekumar Chalishajar,
  • Dhanalakshmi Kasinathan,
  • Ravikumar Kasinathan,
  • Ramkumar Kasinathan

摘要

In this manuscript, we investigate a class of fractional stochastic differential equations driven by time-changed Brownian motion (TCBM) with impulsive condition. The existence and uniqueness results are proved in the finite-dimensional space via fixed-point approach. Further, some novel sufficient conditions ensuring the Ulam-Hyer’s Rassias stability (UHRS) in means square by employing the retarded Gronwall-like inequalities. Illustrative examples are provide to obtain theoretical results. Inspired by the interaction between reduced form and structural credit models, we suggest modeling the firm value process as a time-varying Bm that could incorporate stochastic volatility effects and leaps as well as to examine the first passage issue for these kinds of procedures. Utilizing time change structure, the first passage problem for stochastic processes reveals that the distribution functions are efficiently calculable in a variety of practical instances.