Let $X_t$ be a multivariate OU process and $Y_t$ be the Gaussian process defined by $$ Y_t = \int_0^t X_s ds + W_t, $$ for some Brownian motion independent of $X_t$. Let $a>0$; is there a large deviation result, describing the hitting time of $Y_t$ to $a$?

I've seen similar results in other papers, for example here but I can't seem to find this type of result...

More precisely, if $a\geq 0$ and $\tau_a$ is the hitting time defined by $$ \tau_a\triangleq inf \left\{ t>0: \, |Y_t|\leq a \right\}, $$ then is there a result quantifying $f$ where $f$ satisfies a large-deviation principle of the form $$ \ln \mathbb{P}\left( \tau_a >x \right) \leq f(x) , $$ and $f(x)$ is a $C^1$-function of $x$.

Let $X_t$ be an OU process and $Y_t$ be the Gaussian process defined by $$ Y_t = y+\int_0^t X_s ds + W_t, $$ for some Brownian motion independent of $X_t$. Let $y,a>0$; is there a large deviation result, describing the hitting time of $Y_t$ to $a$?

I've seen similar results in other papers, for example here but I can't seem to find this type of result...

More precisely, if $a\geq 0$ and $\tau_a$ is the hitting time defined by $$ \tau_a\triangleq inf \left\{ t>0: \, |Y_t|\leq a \right\}, $$ then is there a result quantifying $f$ where $f$ satisfies a large-deviation principle of the form $$ \ln \mathbb{P}\left( \tau_a >x \right) \leq f(x) , $$ and $f(x)$ is a $C^1$-function of $x$.

Let $X_t$ be a multivariate OU process and $Y_t$ be the Gaussian process defined by $$ Y_t = \int_0^t X_s ds + W_t, $$ for some Brownian motion independent of $X_t$. Let $a>0$; is there a large deviation result, describing the hitting time of $Y_t$ to $a$?

I've seen similar results in other papers, for example here but I can't seem to find this type of result...

More precisely, if $a\geq 0$ and $\tau_a$ is the hitting time defined by $$ \tau_a\triangleq \left\{ t>0: \, |Y_t|\leq a \right\}, $$ then is there a result quantifying $f$ where $f$ satisfies a large-deviation principle of the form $$ \ln \mathbb{P}\left( \tau_a >x \right) \leq f(x) , $$ and $f(x)$ is a $C^1$-function of $x$.

Let $X_t$ be a multivariate OU process and $Y_t$ be the Gaussian process defined by $$ Y_t = \int_0^t X_s ds + W_t, $$ for some Brownian motion independent of $X_t$. Let $a>0$; is there a large deviation result, describing the hitting time of $Y_t$ to $a$?

I've seen similar results in other papers, for example here but I can't seem to find this type of result...

More precisely, if $a\geq 0$ and $\tau_a$ is the hitting time defined by $$ \tau_a\triangleq inf \left\{ t>0: \, |Y_t|\leq a \right\}, $$ then is there a result quantifying $f$ where $f$ satisfies a large-deviation principle of the form $$ \ln \mathbb{P}\left( \tau_a >x \right) \leq f(x) , $$ and $f(x)$ is a $C^1$-function of $x$.