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- W2950871141 abstract "We consider a process $(X_t)_{tin[0,T)}$ given by the SDE $dX_t = alpha b(t)X_t dt + sigma(t) dB_t$, $tin[0,T)$, with initial condition $X_0=0$, where $Tin(0,infty]$, $alphain R$, $(B_t)_{tin[0,T)}$ is a standard Wiener process, $b:[0,T)to Rsetminus{0}$ and $sigma:[0,T)to(0,infty)$ are continuously differentiable functions. Assuming that $b$ and $sigma$ satisfy a certain differential equation we derive an explicit formula for the joint Laplace transform of $int_0^tfrac{b(s)^2}{sigma(s)^2}(X_s)^2 ds$ and $(X_t)^2$ for all $tin[0,T)$. As an application, we study asymptotic behavior of the maximum likelihood estimator of $alpha$ for $sign(alpha-K)=sign(K)$, $Kne0$, and for $alpha=K$, $Kne0$. As an example, we examine the so-called $alpha$-Wiener bridges given by SDE $dX_t = -frac{alpha}{T-t}X_t dt + dB_t$, $tin[0,T)$, with initial condition $X_0=0$." @default.
- W2950871141 created "2019-06-27" @default.
- W2950871141 creator A5007164445 @default.
- W2950871141 creator A5077585544 @default.
- W2950871141 date "2008-10-16" @default.
- W2950871141 modified "2023-09-27" @default.
- W2950871141 title "Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions" @default.
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