Search results

Stochastic control refers to the general area in which some random variable distributi ...value of some given function evaluated at the end point of the stochastic process. ...

The optimal stopping is a problem in the context of optimal [[stochastic control]] whose solution is obtained through the [[obstacle problem]]. The setting is the following. There is a stochastic process $X_t$ and we have the choice of stopping it at any time $\tau$. When we sto ...

A Lévy process is an important type of [[stochastic process]] (namely, a family of $\mathbb{R}^d$ valued random variables each indexed ...Poisson process]], the trajectory described by typical sample path of this process would look like the union of several disconnected Brownian motion paths. ...

...ch that kind of equations occur. An important example is the problems in [[stochastic control]], which motivate the study of [[fully nonlinear integro-differenti ...rabolic equations, but one often encounters nontrivial difficulties in the process. In these equations, we also find some form of [[maximum principle]] and [[ ...

...}$, we consider a stochastic Poisson jump $\{ \eta_t\}_{t\in\mathbb{R}_+}$ process with values in $\Lambda_\gamma$ and which is generated by the operator ...

The same equation can be derived from a [[stochastic control]] problem called [[optimal stopping problem]]. This is a model in [ Given a [[Levy process]] $X_t$ we consider the following problem. We want to find the optimal stop ...

...ic control]] known as the [[optimal stopping problem]]. We follow a [[Levy process]] $X(t)$ with generator $L$ (assume it is linear). We are allowed to stop a ...hi(x)$. If $x \in \Omega$, we have the choice to either stop of follow the process. If we choose to stop, we get $u(x)=\varphi(x)$. If we choose to continue, ...

...nsider diffusions other than Brownian motion. If $X^x_t$ is the stochastic process given by the SDE: $X_0^x = x$ and $dX_t^x = \sigma(X) dB$, and we define as Nonlinear equations arise from [[stochastic control]] problems. Say that we can choose the coefficients $a_{ij}(x)$ fro ...

...nce. The fractional Laplacian is just the particular case when the [[Levy process]] involved is $\alpha$-stable and radially symmetric. The optimal regularit ...