The 𝒮-Transform of Sub-fBm and an Application to a Class of Linear Subfractional BSDEs
Let SH be a subfractional Brownian motion with index 0<H<1. Based on the 𝒮-transform in white noise analysis we study the stochastic integral with respect to SH, and we also prove a Girsanov theorem and derive an Itô formula. As an application we study the solutions of backward stochastic diff...
| Published in: | Advances in Mathematical Physics |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Online Access: | http://dx.doi.org/10.1155/2013/827192 |
| Summary: | Let SH be a subfractional Brownian motion with index 0<H<1. Based on the 𝒮-transform in white noise analysis we study the stochastic integral with respect to SH, and we also prove a Girsanov theorem and derive an Itô formula. As an application we study the solutions of backward stochastic differential equations driven by SH of the form -dYt=f(t,Yt,Zt)dt-ZtdStH, t∈[0,T],YT=ξ, where the stochastic integral used in the above equation is Pettis integral. We obtain the explicit solutions of this class of equations under suitable assumptions. |
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| ISSN: | 1687-9120 1687-9139 |