论文标题
UMD Banach空间中的向后随机演变夹杂物
Backward Stochastic Evolution Inclusions in UMD Banach Spaces
论文作者
论文摘要
在本文中，我们证明了对向后的随机演变包含（简称BSEI）的温和$ l^p $ - solution \ begin \ begin {align*}％\ label {bsdi3} \ begin {case} dy_t+ay_tdt \ in G（t，y_t，z_t）dt+z_tdw_t，\ quad t \ in [0，t] y_t =ξ， \ end {cases} \ end {align*}其中$ w =（w_t）_ {t \ in [0，t]} $是一种标准的布朗尼运动，$ a $是$ c_0 $ -semigroup的生成器，$ c_0 $ - semigroup在umd banach space $ e $，$ e $，$ e $的条件下，是$ l^p（f \ e），f \ em， $ p> 1 $和$ g $是满足某些适当条件的设定值功能。 还研究了带有Martingale型2美元的空间中值的过程的情况。
In this paper, we prove the existence of a mild $L^p$-solution for the backward stochastic evolution inclusion (BSEI for short) of the form \begin{align*}%\label{BSDI3} \begin{cases} dY_t+AY_tdt\in G(t,Y_t,Z_t)dt+Z_tdW_t,\quad t\in [0,T] Y_T =ξ, \end{cases} \end{align*} where $W=(W_t)_{t\in [0,T]}$ is a standard Brownian motion, $A$ is the generator of a $C_0$-semigroup on a UMD Banach space $E$, $ξ$ is a terminal condition from $L^p(Ω,\mathscr{F}_T;E)$, with $p>1$ and $G$ is a set-valued function satisfying some suitable conditions. The case when the processes with values in spaces that have martingale type $2$, has been also studied.
