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In reference to film and television, drama is a genre of narrative fiction (or semi-fiction) intended to be more serious than humorous in tone. [1] Drama of this kind is usually qualified with additional terms that specify its particular subgenre, such as "police crime drama", "political drama", "legal drama", "historical period drama", "domestic drama", or "comedy-drama". These terms tend to indicate a particular setting or subject-matter, or else they qualify the otherwise serious tone of a drama with elements that encourage a broader range of moods. All forms of cinema or television that involve fictional stories are forms of drama in the broader sense if their storytelling is achieved by means of actors who represent ( mimesis ) characters. In this broader sense, drama is a mode distinct from novels, short stories, and narrative poetry or songs. [2] In the modern era before the birth of cinema or television, "dram...

Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite Let $(W_s)_s geq 0$ be a Wiener process and $tau$ be a random variable with an exponential distribution with parameter $lambda$. Suppose that $W$ and $tau$ are independent. In this question, we see that the distribution of the stopped Wiener process $W_tau$ corresponds to a Laplace distribution with scale parameter $fracsigmasqrt2lambda$ where $sigma$ is the instantaneous variance of the Wiener process. Suppose now, that the variance $sigma^2$ also follows a stochastic process such that we have: $$dS = sigma SdW_s \ dsigma^2 = alphasigma^2dt + xisigma^2dW_sigma$$ where $alpha$ and $xi$ are independent of $S$ and $dW_s$ and $dW_sigma$ are independent Wiener processes. My aim is to derive the distribution of $log S_tau$. First, if $barV_T$ denotes the mean variance over some time interval $[0,T]$ defined by $$barV_T = frac1T intlimits_0^Tsigma^2(t)dt,$$ it is easy to show (Lemma of Îto) that $$...