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Mehrdoust, Farshid, Karimi, Arezou. (1404). On the Existence and Uniqueness of Solutions to Rough Fractional Stochastic Differential Equations. سامانه مدیریت نشریات علمی, (), 31-44. doi: 10.22054/jmmf.2025.86744.1194
Farshid Mehrdoust; Arezou Karimi. "On the Existence and Uniqueness of Solutions to Rough Fractional Stochastic Differential Equations". سامانه مدیریت نشریات علمی, , , 1404, 31-44. doi: 10.22054/jmmf.2025.86744.1194
Mehrdoust, Farshid, Karimi, Arezou. (1404). 'On the Existence and Uniqueness of Solutions to Rough Fractional Stochastic Differential Equations', سامانه مدیریت نشریات علمی, (), pp. 31-44. doi: 10.22054/jmmf.2025.86744.1194
Mehrdoust, Farshid, Karimi, Arezou. On the Existence and Uniqueness of Solutions to Rough Fractional Stochastic Differential Equations. سامانه مدیریت نشریات علمی, 1404; (): 31-44. doi: 10.22054/jmmf.2025.86744.1194

On the Existence and Uniqueness of Solutions to Rough Fractional Stochastic Differential Equations

Journal of Mathematics and Modeling in Finance
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 آذر 1404    اصل مقاله (203.22 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22054/jmmf.2025.86744.1194
نویسندگان
Farshid Mehrdoust* 1؛ Arezou Karimi2
1Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan
2Mathematical Science, Applied Mathematics
چکیده
Precise modeling of financial asset volatility is significant for robust risk management and derivative pricing‎. ‎Recent scholarly investigations have demonstrated a significant interest in employing stochastic processes with short-term memory for this purpose‎. ‎Consequently‎, ‎rigorous examination of the existence and uniqueness of solutions for these processes assumes critical importance‎. ‎This study commences with the precise definition of a fractional operator for $H \in(0‎, ‎\frac{1}{2})$‎. ‎Subsequently‎, ‎the finiteness of the second-order moment of the Itô-Skorokhod integral is meticulously investigated‎, ‎utilizing the aforementioned operator‎, ‎specifically within the range of $H \in(0‎, ‎\frac{1}{2})$‎. ‎Ultimately‎, ‎leveraging this moment and rigorously applying Lipschitz and linear growth conditions‎, ‎and through the application of Gronwall's inequality‎, ‎the existence and uniqueness of solutions for stochastic differential equations with short-term memory are definitively established‎.
کلیدواژه‌ها
Fractional Brownian motion‎؛ ‎Wiener integral‎؛ ‎Stochastic differential equations‎؛ ‎Lipschitzian condition؛ Gronwall' s inequality
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تعداد مشاهده مقاله: 86
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